{"papers":[{"url":"https://www.semanticscholar.org/paper/On-the-LambertW-function-Corless-Gonnet/2bc0144228ecee16e40dc94a085cd85bb1541c8e?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"On the LambertW function","authors":[{"name":"Robert M. Corless","url":"https://www.semanticscholar.org/author/Robert-M-Corless/2119294"},{"name":"Gaston H. Gonnet","url":"https://www.semanticscholar.org/author/Gaston-H-Gonnet/3134435"},{"name":"D. E. G. Hare","url":"https://www.semanticscholar.org/author/D-E-G-Hare/8809713"},{"name":"David J. Jeffrey","url":"https://www.semanticscholar.org/author/David-J-Jeffrey/3350328"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Adv. Comput. Math.","year":1996,"stats":{"influentialCitations":27,"estimatedTotalCitations":{"min":1677.4427594703297,"value":1925.4427594703297,"max":2206.4427594703297,"confidence":0.9},"velocity":{"min":148.34181399292544,"value":160.26277427220342,"max":173.76999136283692,"confidence":0.9},"acceleration":{"min":0.02857142857142864,"value":0.02857142857142862,"max":0.028571428571428678,"confidence":0.9}},"journal":{"name":"Adv. Comput. Math.","volume":"5","pages":"329-359"},"paperAbstract":"The Lambert W function is deened to be the multivalued inverse of the function w 7 ! we w. It has many applications in pure and applied mathematics, some of which are brieey described here. We present a new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an eecient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W.","sourceIds":["journals/adcm/CorlessGHJK96"]},{"url":"https://www.semanticscholar.org/paper/The-Art-of-Computer-Programming-Volume-III-Sorting-Knuth/9a925d73aae2b8c1aa6b4eb2a90d2d93c8d5e3c4?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Art of Computer Programming, Volume III: Sorting and Searching","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1973,"stats":{"influentialCitations":110,"estimatedTotalCitations":{"min":5643.440553020881,"value":6045.440553020881,"max":6474.440553020881,"confidence":0.9},"velocity":{"min":164.5499527097381,"value":171.12915418113275,"max":178.15024231851658,"confidence":0.9},"acceleration":{"min":-0.06508875739644973,"value":-0.06508875739644977,"max":-0.06508875739644981,"confidence":0.9}},"sourceIds":["books/aw/Knuth73"]},{"url":"https://www.semanticscholar.org/paper/Fast-Pattern-Matching-in-Strings-Knuth-Morris/44799559a1067e06b5a6bf052f8f10637707928f?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Fast Pattern Matching in Strings","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"James H. Morris","url":"https://www.semanticscholar.org/author/James-H-Morris/17023686"},{"name":"Vaughan R. Pratt","url":"https://www.semanticscholar.org/author/Vaughan-R-Pratt/1691192"}],"venue":"SIAM J. Comput.","year":1977,"stats":{"influentialCitations":25,"estimatedTotalCitations":{"min":2165.0938599842398,"value":2399.0938599842398,"max":2658.0938599842398,"confidence":0.9},"velocity":{"min":104.49284216465036,"value":110.76681018875728,"max":117.71107394193545,"confidence":0.9},"acceleration":{"min":-0.04672897196261679,"value":-0.04672897196261678,"max":-0.04672897196261678,"confidence":0.9}},"journal":{"name":"SIAM J. Comput.","volume":"6","pages":"323-350"},"paperAbstract":"An algorithm is presented which finds all occurrences of one. given string within another, in running time proportional to the sum of the lengths of the strings. The constant of proportionality is low enough to make this algorithm of practical use, and the procedure can also be extended to deal with some more general pattern-matching problems. A theoretical application of the algorithm shows that the set of concatenations of even palindromes, i.e., the language {can}*, can be recognized in linear time. Other algorithms which run even faster on the average are also considered. Text-editing programs are often required to search through a string of characters looking for instances of a given \"pattern\" string; we wish to find all positions, or perhaps only the leftmost position, in which the pattern occurs as a contiguous substring of the text. For example, c a e n a r y contains the pattern e n, but we do not regard c a n a r y as a substring. The obvious way to search for a matching pattern is to try searching at every starting position of the text, abandoning the search as soon as an incorrect character is found. But this approach can be very inefficient, for example when we are looking for an occurrence of aaaaaaab in aaaaaaaaaaaaaab. When the pattern is a\"b and the text is a2\"b, we will find ourselves making (n + 1) comparisons of characters. Furthermore, the traditional approach involves \"backing up\" the input text as we go through it, and this can add annoying complications when we consider the buffering operations that are frequently involved. In this paper we describe a pattern-matching algorithm which finds all occurrences of a pattern of length rn within a text of length n in O(rn + n) units of time, without \"backing up\" the input text. The algorithm needs only O(m) locations of internal memory if the text is read from an external file, and only O(log m) units of time elapse between consecutive single-character inputs. All of the constants of proportionality implied by these \"O\" formulas are independent of the alphabet size.","sourceIds":["journals/siamcomp/KnuthMP77"]},{"url":"https://www.semanticscholar.org/paper/The-art-of-computer-programming-Volume-II-Seminume-Knuth/a83a16010825d9ba9d57baf5a5ff52347b684d6c?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The art of computer programming, Volume II: Seminumerical Algorithms, 3rd Edition","authors":[{"name":"Donald Ervin Knuth","url":"https://www.semanticscholar.org/author/Donald-Ervin-Knuth/10772633"}],"venue":"","year":1998,"stats":{"influentialCitations":20,"estimatedTotalCitations":{"min":651.4051383383768,"value":786.4051383383768,"max":948.4051383383768,"confidence":0.9},"velocity":{"min":30.03583198800993,"value":33.35051477261988,"max":37.32813411415183,"confidence":0.9},"acceleration":{"min":-0.09090909090909083,"value":-0.09090909090909086,"max":-0.09090909090909093,"confidence":0.9}},"journal":{"pages":"I-XIII, 1-762"},"sourceIds":["books/lib/Knuth98"]},{"url":"https://www.semanticscholar.org/paper/The-art-of-computer-programming-Volume-I-Fundament-Knuth/6b2a23349099f95c1c4850bb1d4731612a7046e6?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The art of computer programming, Volume I: Fundamental Algorithms, 3rd Edition","authors":[{"name":"Donald Ervin Knuth","url":"https://www.semanticscholar.org/author/Donald-Ervin-Knuth/10772633"}],"venue":"","year":1997,"stats":{"influentialCitations":24,"estimatedTotalCitations":{"min":862.2741674839956,"value":1015.2741674839956,"max":1194.2741674839956,"confidence":0.9},"velocity":{"min":57.04668312769638,"value":62.71963969013101,"max":69.35662808670487,"confidence":0.9},"acceleration":{"min":-0.1538461538461538,"value":-0.15384615384615385,"max":-0.1538461538461539,"confidence":0.9}},"journal":{"pages":"I-XIX, 1-650"},"sourceIds":["books/lib/Knuth97"]},{"url":"https://www.semanticscholar.org/paper/The-Birth-of-the-Giant-Component-Janson-Knuth/3e2d96652b9170c70e781d0eb91ba7da963b9c3a?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Birth of the Giant Component","authors":[{"name":"Svante Janson","url":"https://www.semanticscholar.org/author/Svante-Janson/1732375"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Tomasz Luczak","url":"https://www.semanticscholar.org/author/Tomasz-Luczak/1698759"},{"name":"Boris Pittel","url":"https://www.semanticscholar.org/author/Boris-Pittel/1716582"}],"venue":"Random Struct. Algorithms","year":1993,"stats":{"influentialCitations":8,"estimatedTotalCitations":{"min":241.08840326666132,"value":305.0884032666613,"max":389.0884032666613,"confidence":0.9},"velocity":{"min":9.60737366228432,"value":10.935068217443055,"max":12.677667321088895,"confidence":0.9},"acceleration":{"min":0.0,"value":0.0,"max":0.0,"confidence":0.9}},"journal":{"name":"Random Struct. Algorithms","volume":"4","pages":"233-359"},"sourceIds":["journals/rsa/JansonKLP93"]},{"url":"https://www.semanticscholar.org/paper/Structured-Programming-with-go-to-Statements-Knuth/3fdae4603265209ddf420cfaa9cbd0286c567c6c?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Structured Programming with go to Statements","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"ACM Comput. Surv.","year":1974,"stats":{"influentialCitations":7,"estimatedTotalCitations":{"min":541.1147009624382,"value":681.1147009624382,"max":854.1147009624382,"confidence":0.9},"velocity":{"min":23.29606077741077,"value":26.48779392631704,"max":30.431864174608364,"confidence":0.9},"acceleration":{"min":-0.21739130434782614,"value":-0.2173913043478261,"max":-0.21739130434782608,"confidence":0.9}},"journal":{"name":"ACM Comput. Surv.","volume":"6","pages":"261-301"},"paperAbstract":"A consideration of several different examples sheds new light on the problem of ereat-ing reliable, well-structured programs that behave efficiently. This study focuses largely on two issues: (a) improved syntax for iterations and error exits, making it possible to write a larger class of programs clearly and efficiently without go to statements ; (b) a methodology of program design, beginning with readable and correct, but possibly inefficient programs that are systematically transformed if necessary into efficient and correct, but possibly less readable code. The discussion brings out opposing points of view about whether or not go to statements should be abolished; some merit is found on both sides of this question. Fina!ly, an attempt is made to define the true nature of structured programming, and to recommend fruitful directions for further study. You may go when you will go, And I will stay behind. Most likely you go your way and I'll go mine.","sourceIds":["journals/csur/Knuth74"]},{"url":"https://www.semanticscholar.org/paper/On-the-Translation-of-Languages-from-Left-to-Rigth-Knuth/fc230d6b4e6d275bff21b64dd0f457f07a92055f?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"On the Translation of Languages from Left to Rigth","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Information and Control","year":1965,"stats":{"influentialCitations":5,"estimatedTotalCitations":{"min":471.03763616423646,"value":574.0376361642365,"max":700.0376361642365,"confidence":0.9},"velocity":{"min":18.865943310439636,"value":21.060080991350393,"max":23.74417174663928,"confidence":0.9},"acceleration":{"min":-0.039999999999999994,"value":-0.03999999999999998,"max":-0.03999999999999999,"confidence":0.9}},"journal":{"name":"Information and Control","volume":"8","pages":"607-639"},"paperAbstract":"There has been much recent interest in languages whose grammar is sufficiently simple that an efficient left-to-right parsing algorithm can be mechanically produced from the grammar. In this paper, we define LR(k) grammars, which are perhaps the most general ones of this type, and they provide the basis for understanding all of the special tricks which have been used in the construction of parsing algorithms for languages with simple structure, e.g. algebraic languages. We give algorithms for deciding if a given grammar satisfies the LR (k) condition, for given k, and also give methods for generating recognizers for LR(k) grammars. It is shown that the problem of whether or not a grammar is LR(k) for some k is undecidable, and the paper concludes by establishing various connections between LR(k) grammars and deterministic languages. In particular, the LR(]c) condition is a natural analogue, for grammars, of the deterministic condition, for languages. I. INTI~ODUCTION AND DEFINITIONS The word \"language\" will be used here to denote a set of character strings which has been variously called a context free language, a (simple) phrase structure language, a constituent-structure language, a definable set, a BNF language, a Chomsky type 2 (or type 4) language, a push-down automaton language, etc. Such languages have aroused wide interest because they serve as approximate models for natural languages and computer programming languages, among others. In this paper we single out an important class of languages wl~fich will be called translatable from left to right; this means if we read the characters of a string from left to right, and look a given finite number of characters ahead , we are able to parse the given string without ever backing up to consider a previous decision. Such languages are particularly important in the case of computer programming, since this condition means a parsing algorithm can be mechanically constructed which requires an execution time at worst proportional to the length of the string being parsed. Special-purpose 607","sourceIds":["journals/iandc/Knuth65"]},{"url":"https://www.semanticscholar.org/paper/Literate-Programming-Knuth/81ecd7489020252e34ff8e5e82ca98964b9b3135?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Literate Programming","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Comput. J.","year":1984,"stats":{"influentialCitations":16,"estimatedTotalCitations":{"min":616.2551858760686,"value":741.2551858760686,"max":891.2551858760686,"confidence":0.9},"velocity":{"min":24.487627139413714,"value":27.24271195954782,"max":30.54881374370875,"confidence":0.9},"acceleration":{"min":-0.29032258064516125,"value":-0.29032258064516125,"max":-0.2903225806451612,"confidence":0.9}},"journal":{"name":"Comput. J.","volume":"27","pages":"97-111"},"paperAbstract":"The author and his associates have been experimenting for the past several years with a programming language and documentation system called WEB. This paper presents WEB by example, and discusses why the new system appears to be an improvement over previous ones. The past ten years have witnessed substantial improvements in programming methodology. This advance, carried out under the banner of \" structured programming , \" has led to programs that are more reliable and easier to comprehend; yet the results are not entirely satisfactory. My purpose in the present paper is to propose another motto that may be appropriate for the next decade, as we attempt to make further progress in the state of the art. I believe that the time is ripe for significantly better documentation of programs, and that we can best achieve this by considering programs to be works of literature. Hence, my title: \" Literate Programming. \" Let us change our traditional attitude to the construction of programs: Instead of imagining that our main task is to instruct a computer what to do, let us concentrate rather on explaining to human beings what we want a computer to do. The practitioner of literate programming can be regarded as an essayist, whose main concern is with exposition and excellence of style. Such an author, with thesaurus in hand, chooses the names of variables carefully and explains what each variable means. He or she strives for a program that is comprehensible because its concepts have been introduced in an order that is best for human understanding, using a mixture of formal and informal methods that re¨ınforce each other. I dare to suggest that such advances in documentation are possible because of the experiences I've had during the past several years while working intensively on software development. By making use of several ideas that have existed for a long time, and by applying them systematically in a slightly new way, I've stumbled across a method of composing programs that excites me very much. In fact, my enthusiasm is so great that I must warn the reader to discount much of what I shall say as the ravings of a fanatic who thinks he has just seen a great light. Programming is a very personal activity, so I can't be certain that what has worked for me will work for everybody. Yet the impact of this new approach on …","sourceIds":["journals/cj/Knuth84"]},{"url":"https://www.semanticscholar.org/paper/The-Art-of-Computer-Programming-Volume-II-Seminume-Knuth/a0c6bd744a82dca055731df419d552578058b7d6?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Art of Computer Programming, Volume II: Seminumerical Algorithms, 2nd Edition","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1981,"stats":{"influentialCitations":50,"estimatedTotalCitations":{"min":1652.4526976669924,"value":1857.4526976669924,"max":2087.452697666992,"confidence":0.9},"velocity":{"min":36.55268003096366,"value":39.13803611664475,"max":42.03867952984792,"confidence":0.9},"acceleration":{"min":-0.3023255813953488,"value":-0.3023255813953489,"max":-0.3023255813953488,"confidence":0.9}},"sourceIds":["books/aw/Knuth81"]},{"url":"https://www.semanticscholar.org/paper/The-Stanford-GraphBase-a-platform-for-combinatoria-Knuth/b9dc985b40ab9146093e7088f012db99e8d7172b?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Stanford GraphBase - a platform for combinatorial computing","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1993,"stats":{"influentialCitations":11,"estimatedTotalCitations":{"min":664.9478161761955,"value":814.9478161761955,"max":995.9478161761955,"confidence":0.9},"velocity":{"min":55.568246681025556,"value":62.23770384094934,"max":70.2855154805907,"confidence":0.9},"acceleration":{"min":0.15789473684210528,"value":0.15789473684210525,"max":0.1578947368421052,"confidence":0.9}},"journal":{"pages":"I-VII, 1-576"},"paperAbstract":"A highly portable collection of programs and data is now available to researchers who study combinatorial algorithms and data structures. All files are in the public domain and usable with only one restriction: They must not be changed! A \" change file \" mechanism allows local customization while the master files stay intact. The programs are intended to be interesting in themselves as examples of \" literate programming. \" Thus, the Stanford GraphBase can also be regarded as a collection of approximately 30 essays for programmers to enjoy reading, whether or not they are doing algorithmic research. The programs are written in CWEB, a combination of T E X and C that is easy to use by anyone who knows those languages and easy to read by anyone familiar with the rudiments of C. (The CWEB system is itself portable and in the public domain.) Four program modules constitute the kernel of the GraphBase: gb flip is a portable random number generator; gb graph defines standard data structures for graphs and includes routines for storage allocation ; gb io reads data files and makes sure they are uncorrupted; gb sort is a portable sorting routine for 32-bit keys in linked lists of nodes. All of the other programs rely on gb graph and some subset of the other three parts of the kernel. A dozen or so generator modules construct graphs that are of special interest in algorithmic studies. For example, gb basic contains 12 subroutines to produce standard graphs, such as the graphs of queen moves on d-dimensional rectangular boards with \" wrap-around \" on selected coordinates. Another generator module, gb rand, produces several varieties of random graphs. Each graph has a unique identifier that allows researchers all over the world to work with exactly the same graphs, even when those graphs are \" random. \" Repeatable experiments and standard benchmarks will therefore be possible and widely available. Most of the generator modules make use of data sets, which the author has been collecting for 20 years in an attempt to provide interesting and instructive examples for some forthcoming books on combinatorial algorithms (The Art of Computer Programming, Volumes 4A, 4B, and 4C). For example, one of the data sets is words.dat, a collection of 5-letter words of English that the author believes is \" complete \" from his own reading experience. Each word is accompanied by frequency counts …","sourceIds":["books/daglib/0071477"]},{"url":"https://www.semanticscholar.org/paper/The-Art-of-Computer-Programming-Volume-I-Fundament-Knuth/08e6eca6d996d840498816f8febae02337509b86?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1973,"stats":{"influentialCitations":19,"estimatedTotalCitations":{"min":907.5787910253073,"value":1071.5787910253073,"max":1263.5787910253073,"confidence":0.9},"velocity":{"min":13.091088341306014,"value":14.397411779610655,"max":15.926766048845357,"confidence":0.9},"acceleration":{"min":0.16666666666666657,"value":0.1666666666666666,"max":0.16666666666666657,"confidence":0.9}},"journal":{"pages":"I-XXI, 1-634"},"sourceIds":["books/aw/Knuth73a"]},{"url":"https://www.semanticscholar.org/paper/The-Art-of-Computer-Programming-Volume-II-Seminume-Knuth/0a5ae7306a68fc3b96302c1cd645c86341b73aee?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Art of Computer Programming, Volume II: Seminumerical Algorithms","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1969,"stats":{"influentialCitations":20,"estimatedTotalCitations":{"min":1285.7283563316646,"value":1496.7283563316646,"max":1737.7283563316646,"confidence":0.9},"velocity":{"min":51.38424493701186,"value":56.09041177574286,"max":61.46570186168679,"confidence":0.9},"acceleration":{"min":-0.09523809523809515,"value":-0.0952380952380952,"max":-0.09523809523809525,"confidence":0.9}},"journal":{"pages":"I-XI, 1-624"},"sourceIds":["books/aw/Knuth69"]},{"url":"https://www.semanticscholar.org/paper/The-Art-of-Computer-Programming-Volume-I-Fundament-Knuth/bd3102fa60685380af4c0d9da94237978d40b5bc?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Art of Computer Programming, Volume I: Fundamental Algorithms","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1968,"stats":{"influentialCitations":17,"estimatedTotalCitations":{"min":1040.6430591856526,"value":1204.6430591856526,"max":1394.6430591856526,"confidence":0.9},"velocity":{"min":27.85150805053897,"value":30.342027750120945,"max":33.22738593866103,"confidence":0.9},"acceleration":{"min":-0.3571428571428571,"value":-0.35714285714285715,"max":-0.35714285714285715,"confidence":0.9}},"sourceIds":["books/aw/Knuth68"]},{"url":"https://www.semanticscholar.org/paper/Semantics-of-Context-Free-Languages-Knuth/0b61a17906637ece5a9c5e7e3e6de93378209706?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Semantics of Context-Free Languages","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Mathematical Systems Theory","year":1968,"stats":{"influentialCitations":12,"estimatedTotalCitations":{"min":1614.8660431185604,"value":1807.8660431185604,"max":2024.8660431185604,"confidence":0.9},"velocity":{"min":49.416945007051105,"value":52.884488801951385,"max":56.78322975269418,"confidence":0.9},"acceleration":{"min":-0.2857142857142857,"value":-0.2857142857142857,"max":-0.2857142857142857,"confidence":0.9}},"journal":{"name":"Mathematical Systems Theory","volume":"2","pages":"127-145"},"paperAbstract":"\"Meaning\" may be assigned to a string in a context-free language by defining \"at-tributes\" of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are \"synthe-sized\", i.e., defined solely in terms of attributes of the descendants of the corresponding nonterminal symbol, while other attributes are \"inherited\", i.e., defined in terms of attributes of the ancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature. A simple technique for specifying the \"meaning\" of languages defined by context-free grammars is introduced in Section 1 of this paper, and its basic mathematical properties are investigated in Sections 2 and 3. An example which indicates how the technique can be applied to the formal definition of programming languages is described in Section 4, and finally, Section 5 contains a somewhat biased comparison of the present method to other known techniques for semantic definition. The discussion in this paper is oriented primarily towards programming languages, but the same methods appear to be relevant also in the study of natural languages. 1. Introduction. Let us st/ppose that we want to give a precise definition of binary notation for numbers. This can be done in many ways, and in this section we want to consider a manner of definition which can be generalized so that the meaning of other notations can be expressed in the same way. One such way to define binary notation is to base a definition on","sourceIds":["journals/mst/Knuth68"]},{"url":"https://www.semanticscholar.org/paper/Concrete-mathematics-a-foundation-for-computer-sci-Graham-Knuth/62ed6d4155c9872314d7b67416401344b442fb8f?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Concrete mathematics - a foundation for computer science (2. ed.)","authors":[{"name":"Ronald L. Graham","url":"https://www.semanticscholar.org/author/Ronald-L-Graham/1724174"},{"name":"Donald E. 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Intell.","volume":"6","pages":"293-326"},"sourceIds":["journals/ai/KnuthM75"]},{"url":"https://www.semanticscholar.org/paper/Concrete-mathematics-a-foundation-for-computer-sci-Graham-Knuth/1a6e46c02824033c44433fb43cfb7098df60ac1b?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Concrete mathematics - a foundation for computer science","authors":[{"name":"Ronald L. Graham","url":"https://www.semanticscholar.org/author/Ronald-L-Graham/1724174"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Oren Patashnik","url":"https://www.semanticscholar.org/author/Oren-Patashnik/2819477"}],"venue":"","year":1989,"stats":{"influentialCitations":52,"estimatedTotalCitations":{"min":2159.6858493765567,"value":2388.6858493765567,"max":2641.6858493765567,"confidence":0.9},"velocity":{"min":98.55501567616102,"value":104.34197157963119,"max":110.73542067822486,"confidence":0.9},"acceleration":{"min":-0.07017543859649127,"value":-0.07017543859649125,"max":-0.07017543859649125,"confidence":0.9}},"journal":{"pages":"I-XIII, 1-623"},"sourceIds":["books/daglib/0068021"]},{"url":"https://www.semanticscholar.org/paper/Review-of-Algorithmic-Barriers-Falling-P-NP-by-Don-Gasarch/671baa8d5f405c11a0c27378c9c8017b1b1ed9d8?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of: Algorithmic Barriers Falling: P=NP? by Donald E. Knuth and Edgar G. Daylight and The Essential Knuth by Donald E. Knuth and Edgar G. Daylight","authors":[{"name":"William I. Gasarch","url":"https://www.semanticscholar.org/author/William-I-Gasarch/1740486"}],"venue":"SIGACT News","year":2015,"stats":{},"journal":{"name":"SIGACT News","volume":"46","pages":"21-22"},"sourceIds":["journals/sigact/Gasarch15e"]},{"url":"https://www.semanticscholar.org/paper/14th-Knuth-prize-call-for-nominations-Kannan/d7520ece3e8e94e664f627351396bb8bfb8f33f5?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"14th Knuth prize: call for nominations","authors":[{"name":"Ravi Kannan","url":"https://www.semanticscholar.org/author/Ravi-Kannan/1709080"}],"venue":"SIGACT News","year":2014,"stats":{},"journal":{"name":"SIGACT News","volume":"45","pages":"7-8"},"paperAbstract":"The Donald E. Knuth Prize for outstanding contributions to the foundations of computer science is awarded every 1.5 years by the ACM Special Interest Group on Algorithms and Computing Theory (SIGACT) and the IEEE Technical Committee on the Mathematical Foundations of Computing (TCMFC). The Prize is awarded for major research accomplishments and contributions to the foundations of computer science over an extended period of time. The first Knuth Prize was presented at the 1996 ACM Symposium on Theory of Computing (STOC). Prizes are now presented alternately at STOC and the IEEE Symposium on Foundations of Computer Science (FOCS) with occasional adjustments to ensure that the prize is presented at STOC when STOC is part of the ACM Federated Computing Research Conference. The winner is invited to give a lecture at the conference. The prize is named in honor and recognition of the extraordinary accomplishments of Prof. Donald Knuth, Emeritus at Stanford University. Prof. Knuth is best known for his ongoing multivolume series, \" The Art of Computing Programming, \" which has played a critical role in establishing and defining Computer Science as a rigorous, intellectual discipline. Prof. Knuth has also made fundamental contributions to the subfields of analysis of algorithms, compilers, string matching, term-rewriting systems, literate programming, and typography. His TeX and MF systems are widely accepted as standards for electronic typesetting. Prof. Knuth's work is distinguished by its integration of theoretical analyses and practical, real-world concerns. In his work, theory and practice are not separate components of Computer Science but rather inexorably linked branches of the same whole. The winner will be selected by a Prize Committee consisting of six people appointed by the SIGACT and TCMFC Chairs. The Prize includes a $5000 award and a $1000 travel stipend (for travel to the award ceremony) that are paid by SIGACT and TCMFC. In selecting the Knuth-Prize winner, the Committee will pay particular attention to a sustained record of high-impact, seminal contributions to the foundations of computer science. The selection may also be based partly on educational accomplishments and contributions such as fundamental textbooks and high-quality students. The award is not given for service to the theoretical computer science community, but service might be included in the citation for a winner if appropriate.","sourceIds":["journals/sigact/Kannan14"]},{"url":"https://www.semanticscholar.org/paper/Review-of-selected-papers-on-fun-games-by-Donald-E-Gasarch/085768e8da41b2af6ebc283c25287ded17a33091?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of selected papers on fun & games by Donald E. Knuth","authors":[{"name":"William I. Gasarch","url":"https://www.semanticscholar.org/author/William-I-Gasarch/1740486"}],"venue":"SIGACT News","year":2014,"stats":{},"journal":{"name":"SIGACT News","volume":"45","pages":"17-19"},"sourceIds":["journals/sigact/Gasarch14a"]},{"url":"https://www.semanticscholar.org/paper/Review-of-selected-papers-on-discrete-mathematics-Apon/a4a102cf8785be4236ceb56a5bbceae27511cf1d?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of selected papers on discrete mathematics by Donald E. Knuth","authors":[{"name":"Daniel Apon","url":"https://www.semanticscholar.org/author/Daniel-Apon/1903102"}],"venue":"SIGACT News","year":2014,"stats":{},"journal":{"name":"SIGACT News","volume":"45","pages":"10-13"},"sourceIds":["journals/sigact/Apon14"]},{"url":"https://www.semanticscholar.org/paper/Review-of-companion-to-the-papers-of-Donald-Knuth-Gasarch/06a3deebd8da67428531ab86779e58bd6462c38b?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of companion to the papers of Donald Knuth by Donald E. Knuth","authors":[{"name":"William I. Gasarch","url":"https://www.semanticscholar.org/author/William-I-Gasarch/1740486"}],"venue":"SIGACT News","year":2014,"stats":{},"journal":{"name":"SIGACT News","volume":"45","pages":"19-21"},"sourceIds":["journals/sigact/Gasarch14b"]},{"url":"https://www.semanticscholar.org/paper/Review-of-selected-papers-on-design-of-algorithms-Apon/a2cfd3abe5f2828f52789996e48bcb21e12b03f8?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of selected papers on design of algorithms by Donald E. Knuth","authors":[{"name":"Daniel Apon","url":"https://www.semanticscholar.org/author/Daniel-Apon/1903102"}],"venue":"SIGACT News","year":2014,"stats":{},"journal":{"name":"SIGACT News","volume":"45","pages":"14-16"},"sourceIds":["journals/sigact/Apon14a"]},{"url":"https://www.semanticscholar.org/paper/The-tears-of-Donald-Knuth-Haigh/5d07e10e303ce66ac054149b42124be7b8d50db1?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The tears of Donald Knuth","authors":[{"name":"Thomas Haigh","url":"https://www.semanticscholar.org/author/Thomas-Haigh/1714013"}],"venue":"Commun. ACM","year":2014,"stats":{},"journal":{"name":"Commun. ACM","volume":"58","pages":"40-44"},"paperAbstract":"Has the history of computing taken a tragic turn?","sourceIds":["journals/cacm/Haigh15"]},{"url":"https://www.semanticscholar.org/paper/Don-Knuth-Mastermind-of-Algorithms-review-of-The-a-Strawn/d979731c7af5288143c31572da540fb979e6b266?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Don Knuth: Mastermind of Algorithms [review of \"The art of programming\"]","authors":[{"name":"George Strawn","url":"https://www.semanticscholar.org/author/George-Strawn/2013713"}],"venue":"IT Professional","year":2014,"stats":{},"journal":{"name":"IT Professional","volume":"16","pages":"70-72"},"sourceIds":["journals/itpro/Strawn14d"]},{"url":"https://www.semanticscholar.org/paper/Knuth-s-balancing-of-codewords-revisited-Weber-Immink/2e22d041dd96a84b78684e4ae42ad0a62488e1bb?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Knuth's balancing of codewords revisited","authors":[{"name":"Jos H. Weber","url":"https://www.semanticscholar.org/author/Jos-H-Weber/7410597"},{"name":"Kees A. Schouhamer Immink","url":"https://www.semanticscholar.org/author/Kees-A-Schouhamer-Immink/8393559"}],"venue":"ISIT","year":2008,"stats":{"influentialCitations":1},"journal":{"pages":"1567-1571"},"paperAbstract":"— In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of '1's and '-1's, called balanced codes. Knuth's algorithm is, since look-up tables are absent, well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In our paper we will present results of our attempts to improve the performance of Knuth's balanced codes.","sourceIds":["conf/isit/WeberI08"]},{"url":"https://www.semanticscholar.org/paper/Review-of-Fascicle-4-Generating-All-Trees-History-Weber-Wulff/c50adc0db7513ee604feb6019d3bae56dcec81d1?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of \"Fascicle 4: Generating All Trees - History of Combinatorial Generation by Donald E. Knuth\", Addison-Wesley, 2006, ISBN 0-321-33570-8","authors":[{"name":"Debora Weber-Wulff","url":"https://www.semanticscholar.org/author/Debora-Weber-Wulff/1872140"}],"venue":"ACM SIGSOFT Software Engineering Notes","year":2006,"stats":{},"journal":{"name":"ACM SIGSOFT Software Engineering Notes","volume":"31","pages":"60"},"paperAbstract":"When Will asked for a review of Knuth, I thought that this would be the long-expected Volume 4 in its entirety. I read volumes 1-3 as a student some 30 years ago, volume 1 while in bed with the flu. It was a wonderful way to recover, getting into all of those algorithms. We've had some good stuff since then from Knuth – TeX, Metafont, Stanford GraphBase, John 3:16, but I have been itching to see more from the master, especially since I now myself teach algorithms and data structures at an engineering college. So I learned a new word: fascicle, which means sections of a book, which are published in parts so that they are available before the entire work is finished. This slim volume is 120 pages, and immediately recognizable typographically as a book by Knuth. He gives us some context, explaining the bits that will be coming before this part of volume 4, and then he dives into explaining how to generate all trees. This is related to questions of nested parentheses. He gives some algorithms for randomly (and of course, since this is Knuth, uniformly random) generating trees. A nice idea, but why? Perhaps for testing purposes? I would have liked to see some references to applications of these algorithms here, not just algorithms for the sake of being algorithms. Okay, the Christmas Tree Algorithm is useful for the last lecture before Christmas. He discusses spanning trees, associates Grey codes with trees, and has some connection between trees and lattices – and lost me there. There are many exercises (some are of the research topic variety) and then a very interesting historical note about the 64 hexa-grams in the I Ching. He continues with Indian prosody and Greek poetry metrics, permutations in music and in rolling dice, set partitions , and the Catalan poet Roman Llull (a wonderful palindromic last name), amongst others. This is by far the most fascinating part of this fascicle. The last portion of the book is dedicated to answers to the non-research-topic exercises, a blessing for those mortals amongst us who do not immediately see how to solve these problems. Trees are very important for all sorts of things we do today, from game playing to computer graphics. But this bit of volume 4 is much too theoretical for those who hope to find a quick reference of important combinatorical and …","sourceIds":["journals/sigsoft/Weber-Wulff06"]},{"url":"https://www.semanticscholar.org/paper/Using-bit-recycling-to-reduce-Knuth-s-balanced-cod-Al-Rababa-a-Dube/f01da0770bdc90e3178d7b8b7e9448237cd6ebfe?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Using bit recycling to reduce Knuth's balanced codes redundancy","authors":[{"name":"Ahmad Al-Rababa'a","url":"https://www.semanticscholar.org/author/Ahmad-Al-Rababa-a/1971944"},{"name":"Danny Dube","url":"https://www.semanticscholar.org/author/Danny-Dube/2415512"},{"name":"Jean-Yves Chouinard","url":"https://www.semanticscholar.org/author/Jean-Yves-Chouinard/1701702"}],"venue":"2013 13th Canadian Workshop on Information Theory","year":2013,"stats":{},"journal":{"name":"2013 13th Canadian Workshop on Information Theory","pages":"6-11"},"paperAbstract":"Donald Knuth published an efficient algorithm for constructing a code with balanced codewords. A balanced codeword is a codeword that contains an equal number of zero's and one's. The redundancy of the codes built using Knuth's algorithm is about twice the lower bound on redundancy. In this paper we propose a new scheme based on the bit recycling compression technique to reduce Knuth's algorithm redundancy. The proposed scheme does not affect the simplicity of Knuth's algorithm and achieves less redundancy. Theoretical results and an analysis of our scheme are presented as well.","sourceIds":["conf/cwit/Al-RababaaDC13"]},{"url":"https://www.semanticscholar.org/paper/Validating-the-Knuth-Morris-Pratt-Failure-Function-Gawrychowski-Jez/00f71596f5e9f59132bd9c33bf80abb7399efdae?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Validating the Knuth-Morris-Pratt Failure Function, Fast and Online","authors":[{"name":"Pawel Gawrychowski","url":"https://www.semanticscholar.org/author/Pawel-Gawrychowski/1683786"},{"name":"Artur Jez","url":"https://www.semanticscholar.org/author/Artur-Jez/2987078"},{"name":"Lukasz Jez","url":"https://www.semanticscholar.org/author/Lukasz-Jez/1821870"}],"venue":"Theory of Computing Systems","year":2010,"stats":{},"journal":{"name":"Theory of Computing Systems","volume":"54","pages":"337-372"},"paperAbstract":"Let $\\pi'_{w}$ denote the failure function of the Knuth-Morris-Pratt algorithm for a word w. In this paper we study the following problem: given an integer array $A'[1 \\mathinner {\\ldotp \\ldotp }n]$ , is there a word w over an arbitrary alphabet Σ such that $A'[i]=\\pi'_{w}[i]$ for all i? Moreover, what is the minimum cardinality of Σ required? We give an elementary and self-contained $\\mathcal{O}(n\\log n)$ time algorithm for this problem, thus improving the previously known solution (Duval et al. in Conference in honor of Donald E. Knuth, 2007), which had no polynomial time bound. Using both deeper combinatorial insight into the structure of π′ and advanced algorithmic tools, we further improve the running time to $\\mathcal{O}(n)$ .","sourceIds":["journals/mst/GawrychowskiJJ14","conf/csr/GawrychowskiJJ10"]},{"url":"https://www.semanticscholar.org/paper/DONALD-E-KNUTH-to-receive-the-2011-Abacus-award-fr-Popyack/a6cad7fca8d2de88cd5947ab5b2c7aba7ee2dae6?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"DONALD E. KNUTH to receive the 2011 Abacus award from UPSILON PI EPSILON","authors":[{"name":"Jeffrey L. Popyack","url":"https://www.semanticscholar.org/author/Jeffrey-L-Popyack/3157530"}],"venue":"Inroads","year":2011,"stats":{},"journal":{"name":"Inroads","volume":"2","pages":"26-27"},"paperAbstract":"ming at Stanford, will address the convention attendees following the award presentation. In lieu of a static presentation, Prof. Knuth will conduct an interactive dialog with attendees, entitled \" All Questions Answered \". UPE's most prestigious award acknowledges that while the computing and information disciplines arose in the twentieth century, \" the heritage of computing … stems to the origins of humanity. The Abacus, the earliest and most used calculating device, symbolizes this heritage \" [6]. The Abacus Award was created for the purpose \" of recognizing outstanding individuals who have provided extensive support and leadership for student-related activities in the computing sciences \". Prof. Knuth has been the recipient of most of the major science and related awards including the fi rst ACM Grace Murray Hopper Numerous biographical articles have been written about Prof. Knuth. We refer readers here to an interview published in Stanford Magazine [5], his website [3], and of course, his page on Wikipedia (with the usual disclaimers). These are strongly recommended readings for people intending to attend his Q&A session. Knuth's technical writings in the computing and mathematics fi elds are well known to ACM members. His writings in other fi elds may be less familiar. His book \" 3:16 Bible Texts Illuminated \" [1] resulted from a year-long Bible study series he conducted. Employing a systematic study via stratifi ed sampling, he selected chapter 3, verse 16 from each book of the Bible (for which such a verse exists) and delved into the meaning, backstory, and implications thereof. He has also published transcripts of a series of public lectures on the subject of faith and science, \" Things a Computer Scientist Rarely Talks About \" [2]. Included is a lecture entitled \" God and Computer Science, \" which examines topics from the point of view of a computer scientist. Allow me to conclude with a few tidbits gleaned from the sources cited below: ■ He stands while working at his computers. ■ On a page entitled \" Knuth versus email \" , he says \" I have been a happy man ever since January 1, 1990, when I no longer had an email address. I' d used email since about 1975, and it seems to me that 15 years of email is plenty for one lifetime… Email is a wonderful thing for people whose role in life is to be on top of things. …","sourceIds":["journals/inroads/Popyack11"]},{"url":"https://www.semanticscholar.org/paper/Knuth-s-Balanced-Codes-Revisited-Weber-Immink/782d4a72abd060ddd0f8302bbc4d5e23f1031d01?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Knuth's Balanced Codes Revisited","authors":[{"name":"Jos H. Weber","url":"https://www.semanticscholar.org/author/Jos-H-Weber/7410597"},{"name":"Kees A. Schouhamer Immink","url":"https://www.semanticscholar.org/author/Kees-A-Schouhamer-Immink/8393559"}],"venue":"IEEE Transactions on Information Theory","year":2010,"stats":{},"journal":{"name":"IEEE Transactions on Information Theory","volume":"56","pages":"1673-1679"},"paperAbstract":"In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of ¿1¿s and ¿-1¿s, called balanced codes. Knuth's algorithm is well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In this paper, we will present results of our attempts to improve the performance of Knuth's balanced codes.","sourceIds":["journals/tit/WeberI10"]},{"url":"https://www.semanticscholar.org/paper/Knuth-draws-record-crowd-to-UPE-national-conventio-Popyack/338244d91159b8b05572cab6b5bf6d0fcd0fb0fc?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Knuth draws record crowd to UPE national convention","authors":[{"name":"Jeffrey L. Popyack","url":"https://www.semanticscholar.org/author/Jeffrey-L-Popyack/3157530"}],"venue":"Inroads","year":2011,"stats":{},"journal":{"name":"Inroads","volume":"2","pages":"30-31"},"paperAbstract":"UPE has been a proud sponsor of the ACM International Collegiate Programming Contest since the first World Finals in 1977. This year's competition was scheduled for early March in Sharm el-Sheikh, Egypt, but as the world spotlight turned on the political tensions in Cairo at the end of January, it became increasingly obvious that the Finals could not be held as scheduled. Kudos goes to ICPC Executive Director, William Poucher, for his quick ability to relocate the contest at the end of The UPE National Convention was held during the Friday lunch slot of the SIGCSE Technical Symposium and an estimated 500 people attended it. The business portion of the meeting was kept brief in order to allow maximum time for an address from Abacus Award winner Donald Knuth, to whom credit is certainly due for the record crowd. The meeting consisted of the following items.","sourceIds":["journals/inroads/Popyack11a"]},{"url":"https://www.semanticscholar.org/paper/Companion-to-the-papers-of-Donald-Knuth-Knuth/b5a1b9ba73c1e690389cc317b01b891c3eb7cf0a?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Companion to the papers of Donald Knuth","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"CSLI lecture notes series","year":2012,"stats":{},"journal":{"volume":"202","pages":"I-XIII, 1-441"},"sourceIds":["books/daglib/0030428"]},{"url":"https://www.semanticscholar.org/paper/Review-of-the-art-of-computer-programming-volume-4-Rogers/a442a529b6a4d22728a2853f7cc46e4006dca4c6?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of the art of computer programming: volume 4a by Donald E. Knuth","authors":[{"name":"John D. Rogers","url":"https://www.semanticscholar.org/author/John-D-Rogers/1755756"}],"venue":"SIGACT News","year":2013,"stats":{},"journal":{"name":"SIGACT News","volume":"44","pages":"36-39"},"sourceIds":["journals/sigact/Rogers13"]},{"url":"https://www.semanticscholar.org/paper/Knuth-s-art-of-recovering-from-errors-Staff/7acfa66ac1d56f81466f4c9167f80dd9b7736a11?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Knuth's art of recovering from errors","authors":[{"name":"CACM Staff","url":"https://www.semanticscholar.org/author/CACM-Staff/11135244"}],"venue":"Commun. ACM","year":2008,"stats":{},"journal":{"name":"Commun. ACM","volume":"51","pages":"9"},"paperAbstract":"I REALLy ENjOyED Donald E. Knuth reminiscing in Edward Feigenbaum's interview with him (\" The 'Art' of Being Don-ald Knuth, \" July 2008). Who else would have moved to Stanford University to slow down? Knuth's self-effacing modesty notwithstanding , I would like to challenge anyone to examine the literature preceding Knuth's contribution to algorithms and compiler theory. There was good work, but it was Knuth who set the field on its feet. I'm now looking forward to learning how he \" solves the problem of typesetting \" (see Aug. 2008). I personally made the mistake of using Microsoft Word for my Ph.D. thesis (completed 1996). More recently , I decided that the topic—efficient object-oriented programming for shared-memory multiprocessors—was of interest again due to the rise of mul-ticore computers and reformatted it as a book. What a nightmare. I promised myself I'd use LaTeX for every Ph.D. I ever write again. Dependable Design and the consequences of failure Leah Hoffman's news article \" In Search of Dependable Design \" (July 2008) was a good overview of some of the issues affecting software and system reliability, explaining how system dependability might be improved through good engineering practice. This is similar to a subject I covered in Technology Review (Apr. 1987) on software reliability. However, Hoffman did not adequately discuss the theoretical limits that add to the risk of real-time, interactive applications. Peter Wegner's Communications article \" Why Interaction Is More Powerful Than Algorithms \" (May 1997) pointed out that interaction systems are not only difficult to verify but also formally incomplete, impossible to verify. Where the risk of system failure cannot be further reduced due to such limits, effort must be directed instead at reducing the consequences of failure. technology supports, Doesn't supplant the social compact In \" Information Accountability \" (June 2008), Daniel J. Weitzner et al. so exaggerated the good points they made that they created a false dichot-omy between computing technologies (such as encryption) and societal conventions and laws, summing up in the article's final sentence: \" Technology will better support freedom by relying on these social compacts than by seeking to supplant them. \" They were wrong. Technology does not seek to supplant social compacts but indeed seeks to add to them, legitimately. Proud to Be a member My usual routine on finding Communications in my mailbox is to spend a few minutes flipping through the pages, then …","sourceIds":["journals/cacm/X08k"]},{"url":"https://www.semanticscholar.org/paper/Review-of-mathematics-for-the-analysis-of-algorith-Miksa/f1c0fa26b9283bd98ae9de40113f7260ac760756?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of mathematics for the analysis of algorithms by Daniel H. Greene and Donald E. Knuth","authors":[{"name":"Mladen Miksa","url":"https://www.semanticscholar.org/author/Mladen-Miksa/3250803"}],"venue":"SIGACT News","year":2011,"stats":{},"journal":{"name":"SIGACT News","volume":"42","pages":"12-14"},"paperAbstract":"1 Overview When designing an algorithm it is important to know how well it will perform at a given task. In order to answer that question, we define mathematical equations that describe the relation between performance and input. Most of the time we are interested in the explicit form of that relation, but finding such a form can be a difficult task. Mathematics for the Analysis of Algorithms by Daniel H. Greene and Donald E. Knuth presents a diverse set of mathematical paradigms used for solving those equations. The book consists of four thematically separated chapters covering: binomial identities, recurrence relations, operator methods and asymptotic analysis. The last third of the book contains exams given at Stanford and their solutions, providing additional examples for presented topics. It consists of three midterm and three final exams along with one additional problem. This summary gives a short description of the chapters and is not intended as a comprehensive list of everything described in the book. This chapter is relatively short and to the point. It starts with a summary of useful identities and then proceeds to the description of \" meta \" concepts used in classifying binomial identities (e.g. inverse relations), ending with another list of identities, this time involving harmonic numbers. Some ideas for proving the identities are explained, but the reader is mostly referred to other sources for additional information on the subject. Methods for solving recurrence relations are described in this chapter. They are divided into two major categories: linear and nonlinear relations. The part describing linear relations presents additional subdivisions of types of relations, starting with easier ones and progressing to those more challenging. It describes finite and full history relations with solving techniques varying from trying trial solutions to the repertoire approach. The division of nonlinear relations is not as detailed as that of their linear counterparts, owing to the fact that the methods for solving them are less systematic, as mentioned in the book. Relations covered in this part include relations with maximum or minimum functions, and relations with hidden or approximate linear recurrences.","sourceIds":["journals/sigact/Miksa11"]},{"url":"https://www.semanticscholar.org/paper/Donald-A-Knuth-Scholar-with-a-Passion-for-the-Part-Frenkel/4b5a87ff972649cfcb2d0825d4f41904814922bd?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Donald A. Knuth - Scholar with a Passion for the Particular","authors":[{"name":"Karen A. Frenkel","url":"https://www.semanticscholar.org/author/Karen-A-Frenkel/1706353"}],"venue":"Commun. ACM","year":1987,"stats":{},"journal":{"name":"Commun. ACM","volume":"30","pages":"816-819"},"paperAbstract":"\"Age 30 is kind of appropriate because I got the first copy of volume 1 from the publisher nine days after my 30th birthday. So, a large part of the work had been done when I was 30 years old. They already were working on typesetting the second volume.\"\nCommenting on his books' influence, Knuth says, \"It's been phenomenal from my point of view. In 1976 a study was done of how many people writing papers on computer science made a reference to my book somewhere in their articles, and it was found that about 30 percent of the papers in Communications, Journal of the ACM, and SIAM Journal on Computing cited the book. So it has an impact in that way.\" What about sales? Knuth notes that publishers may joke about professors whose books never sell, but they don't apply here. \"I know that people buy the book. I don't know how many read it. But the sales have been incredible. I think something between 1000 and 2000 copies [have been sold] per month for 20 years.\"","sourceIds":["journals/cacm/Frenkel87b"]},{"url":"https://www.semanticscholar.org/paper/Saddle-Points-in-Random-Matrices-Analysis-of-Knuth-Hofri-Jacquet/818a7fbb4732a4e9713764ae48d45403d4a054dc?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Saddle Points in Random Matrices: Analysis of Knuth Search Algorithms","authors":[{"name":"Micha Hofri","url":"https://www.semanticscholar.org/author/Micha-Hofri/1725884"},{"name":"Philippe Jacquet","url":"https://www.semanticscholar.org/author/Philippe-Jacquet/1698980"}],"venue":"Algorithmica","year":1998,"stats":{},"journal":{"name":"Algorithmica","volume":"22","pages":"516-528"},"paperAbstract":"We present an analysis of algorithms for finding saddle points in a random matrix, presented by Donald E. Knuth as exercise 1.3.2-12 in The Art of Computer Programming. We estimate the average computing costs of three saddle point search algorithms. Amusingly, the asymp-totic results in this analysis about matrix saddle points uses the same approach that leads to the celebrated saddle point method in complex analysis.","sourceIds":["journals/algorithmica/HofriJ98"]},{"url":"https://www.semanticscholar.org/paper/Review-of-Selected-Papers-in-Discrete-Mathematics-Oliveira/780fe636528f724f531b02b1d8f6f8f8ae1165b9?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of \"Selected Papers in Discrete Mathematics by D. Knuth\", CSLI (Center for the Study of Language and Information Publication) paperback, $72.00","authors":[{"name":"Carlos A. S. Oliveira","url":"https://www.semanticscholar.org/author/Carlos-A-S-Oliveira/2034290"}],"venue":"SIGACT News","year":2004,"stats":{},"journal":{"name":"SIGACT News","volume":"35","pages":"11-14"},"paperAbstract":"The book \"Selected Papers in Discrete Mathematics\" is a compilation of work published (plus some unpublished papers) by Donald E. Knuth, in the area of discrete mathematics. Clearly, the author does not need any introduction, and is well known by his authoritative work in areas such analysis of algorithms and digital typography. However, more than this, Knuth is a great example of good expositor and writer. Thus, even if your interests are not directly related to the more mathematical areas of computer science, it is greatly rewarding to read this book as a way of learning how to write good papers.","sourceIds":["journals/sigact/Oliveira04a"]},{"url":"https://www.semanticscholar.org/paper/Review-of-TEX-and-METAFONT-New-Directions-in-Types-Price/7f62b7f3bcfb9fe86ce8e7f3a0ac9b7497b1f909?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of \"TEX and METAFONT, New Directions in Typesetting by Donald Knuth\", Digital Press and the American Mathematical Society","authors":[{"name":"Keith Price","url":"https://www.semanticscholar.org/author/Keith-Price/2888476"}],"venue":"SIGART Newsletter","year":1980,"stats":{},"journal":{"name":"SIGART Newsletter","volume":"71","pages":"28-29"},"paperAbstract":"TEX and METAFONT, New Directions in Typesetting consists of three parts each of which is self-contained. First is \"Mathematical Typography,\" a Gibbs Lecture that Dr. Knuth presented to the annual meeting of the American Mathematical Society. This gives an overview of both TEX and METAFONT and puts them in perspective. Part 2 is a oomplete description of the TEX typesetting system. The last part is a similar description of METAFONT.","sourceIds":["journals/sigart/Price80d"]},{"url":"https://www.semanticscholar.org/paper/A-Proof-of-a-Conjecture-of-Knuth-Paule/23fc966fc1aa4602650e0aea6f58a88c6c049947?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"A Proof of a Conjecture of Knuth","authors":[{"name":"Peter Paule","url":"https://www.semanticscholar.org/author/Peter-Paule/1756682"}],"venue":"Experimental Mathematics","year":1996,"stats":{},"journal":{"name":"Experimental Mathematics","volume":"5","pages":"83-89"},"paperAbstract":"From numerical experiments, D. E. Knuth conjectured that 0 < D n+4 < D n for a combinatorial sequence (D n) defined as the difference D n = R n − L n of two definite hypergeometric sums. The conjecture implies an identity of type L n = R n , involving the floor function. We prove Knuth's conjecture by applying Zeilberger's algorithm as well as classical hypergeometric machinery. 1 The Conjecture In a combinatorial study, D. E. Knuth [8] was led to consider a nontermina-ting hypergeometric series representation of the numbers L n := n k=0 2k k (n ≥ 0). The (ordinary) generating function of (2k k) k≥0 is 1/ √ 1 − 4z, a special instance of the binomial series, and thus ∞ n=0 L n z n = 1/((1 − z) √ 1 − 4z). Expanding 1/(1 − z) as a series in powers of (1 − 4z) and equating like coefficients results in L n = ∞ k=0 4 3 (− 1 3) k k − 1/2 n (−4) n .","sourceIds":["journals/em/Paule96"]},{"url":"https://www.semanticscholar.org/paper/Representing-Graphs-by-Knuth-Trees-Pfaltz/6e45df49f5d0ff6bf29ce693799707da24ae7762?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Representing Graphs by Knuth Trees","authors":[{"name":"John L. Pfaltz","url":"https://www.semanticscholar.org/author/John-L-Pfaltz/2585707"}],"venue":"J. ACM","year":1975,"stats":{},"journal":{"name":"J. ACM","volume":"22","pages":"361-366"},"paperAbstract":"ASSrRACT. By means of the :Knuth transform, arbitrary rooted trees may be represented compactly as binary trees. In this paper it is shown that the domain of this transform may be extended to a much wider class of graphs, while still maintaining its fundamental properties. Graphs, G, belonging to this extended domain are characterized first in terms of properties of an induced graph, G*, and then in terms of local properties of G itself. A classic kind of \"forbidden\" subgraph theorem characterizes nonrepresentable graphs. Finally, it is shown that any directed graph can be modified to make it representable under the transform. Donald Knuth in [2] presents a lovely transformation (which we will call the Knuth transform) by which an arbitrary rooted tree, T~, may be represented as a binary rooted tree, TR, as in Figure 1. It is important because by using such a transform, one can represent any rooted tree, ~ith unbounded out-degree, by a linked data structure in which the cells that represent points of the data structure may be of fixed size. In fact, only two link fields are necessary to completely represent the tree structured relationship between the points. Given such a useful * transformation it is natural to ask, \"Can we apply the Knuth transformation to a larger class of data structures?\" A little experimentation is sufficient to convince us, at least intuitively, that in some cases it can be effectively applied (Figure 2), and in others it cannot (Figure 3). What distinguishes these two graphs? First we must backtrack and define certain concepts with more precision. A directed graph, denoted G = (P, E), is a set P of points (or data items) together with a binary relation, E, (or set of ordered pairs) defined on P. Graphs (we will henceforth drop the adjective \"directed\") are valuable as mathematical models of both abstract data structures and their computer representations. Thus we make a distinction between G~, the graph which models an abstract data structure, and GR, which models (or describes) its computer representation. In many cases the representation is virtually a one-to-one isomorphic copy of the abstract model and the distinction is unimportant. But at other times the distinction may be crucial. A representation is faithful if from GR alone a computer procedure can reproduce all of the information that existed in the abstract model.","sourceIds":["journals/jacm/Pfaltz75"]},{"url":"https://www.semanticscholar.org/paper/Biographies-A-Conversation-with-Don-Knuth-Albers-Steen/906120ba9052ac1f64e465fd47ac1cd91eb09bc2?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Biographies [A Conversation with Don Knuth]","authors":[{"name":"Donald J. Albers","url":"https://www.semanticscholar.org/author/Donald-J-Albers/3051938"},{"name":"Lynn A. Steen","url":"https://www.semanticscholar.org/author/Lynn-A-Steen/2828354"}],"venue":"Annals of the History of Computing","year":1982,"stats":{},"journal":{"name":"Annals of the History of Computing","volume":"4","pages":"257-273"},"paperAbstract":"The Annals is reprinting this interview, more a monologue than a conversation, because Donald E. Knuth is one of the giants of computing. We would like to understand how he developed, what he thought, and how he came by this idea or that as he created his many contributions, not the least of which is the brilliant clarity and comprehensiveness with which he has expresse d and exp lained them. Reprinting is also justified because of the very small intersection between the readership of the Annals and the Two-Year College Mathematics Journal, the original publisher.","sourceIds":["journals/annals/AlbersS82"]},{"url":"https://www.semanticscholar.org/paper/Book-review-Selected-Papers-on-Computer-Science-by-Khuller/98af6be4ad1d14c1479f7a33afca7fff9d190b28?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Book review: Selected Papers on Computer Science by Donald E. Knuth","authors":[{"name":"Samir Khuller","url":"https://www.semanticscholar.org/author/Samir-Khuller/1737147"}],"venue":"SIGACT News","year":1998,"stats":{},"journal":{"name":"SIGACT News","volume":"29","pages":"21-26"},"paperAbstract":"\"Selected papers on computer science\" by Donald E. Knuth [3] is a collection of lectures an d published papers aimed at a wide audience. A detailed narrative, replete with illustrations an d examples, this collection focuses on three principle themes : the centrality of algorithms to compute r science, the importance of combining theory and practice, as well as the historical development o f the field. Addressing the first of these issues, Knuth argues that computer science is essentially abou t algorithms and algorithmic thought. As he puts it, \"Algorithms are the life-blood of compute r science. . .the common denominator that underlies and unifies the different branches\". Defining algorithms as concepts that exist independent of programs, even though programming languages ar e used to express algorithms, Knuth states that \"a person well trained in computer science knows ho w to deal with algorithms, how to construct them, manipulate them, understand them, analyze them\". In fact, in Knuth's view, an attempt to comprehend mathematical concepts as algorithms result s in a far deeper understanding than might ordinarily result. However, even as Knuth underscores the importance of algorithms as a \"general purpose mental tool\" he simultaneously identifies them as a point of difference between computer science and mathematics. Through a series of examples , he demonstrates that while mathematicians are content once they prove that a certain object that satisfies certain properties exists, a Computer Scientist tries to learn how to compute this object. Such a viewpoint, has led to fundamental advances in Computer Science 3. Simpler proofs, as well as alternative proofs and a better understanding of mathematical structures can be achieved whe n one puts on a \"Computer Science hat\". The second theme that Knuth focuses on is the importance of combining theory and practice , something that in his opinion can have a significant payoff for the field as a whole. As he puts is \"the world gets better theoretical tools as it gets better practical tools\". In this context, Knut h specifically points to his experiences in developing METAFONT, and argues that this very practically oriented project generated many interesting new problems and thus had a very profound impact on his research. Some of these problems are discussed in Chapters 6-9. Some sample problems are : solving the K-centers problem on a line (a minor modification of the Frederickson an d Johnson [2]) algorithm solves this problem), …","sourceIds":["journals/sigact/Khuller98a"]},{"url":"https://www.semanticscholar.org/paper/Review-of-The-Art-of-Computer-Programming-Volume-4-Rogers/aec4516259b4796b6dc3481ae2562da4e3a2c156?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Review of \"The Art of Computer Programming, Volume 4, Fascicles 2, 3, and 4 by Donald E. Knuth, \" Pearson Education (Addison-Wesley), 2005","authors":[{"name":"John D. Rogers","url":"https://www.semanticscholar.org/author/John-D-Rogers/1755756"}],"venue":"SIGACT News","year":2008,"stats":{},"journal":{"name":"SIGACT News","volume":"39","pages":"32-35"},"sourceIds":["journals/sigact/Rogers08"]},{"url":"https://www.semanticscholar.org/paper/Book-Review-Selected-Papers-on-Analysis-of-Algorit-Overill/95883be072dbb28866dcaa3b8d4219d908cc3b0c?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Book Review: \"Selected Papers on Analysis of Algorithms\" by Donald E. Knuth","authors":[{"name":"Richard E. Overill","url":"https://www.semanticscholar.org/author/Richard-E-Overill/2506183"}],"venue":"J. Log. Comput.","year":2001,"stats":{},"journal":{"name":"J. Log. Comput.","volume":"11","pages":"355"},"sourceIds":["journals/logcom/Overill01"]},{"url":"https://www.semanticscholar.org/paper/On-obtaining-Knuth-Morris-and-Pratt-s-string-match-Ager-Danvy/56726a9184034eeb0f86845d446bde10f1a04ce1?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"On obtaining Knuth, Morris, and Pratt's string matcher by partial evaluation","authors":[{"name":"Mads Sig Ager","url":"https://www.semanticscholar.org/author/Mads-Sig-Ager/1934628"},{"name":"Olivier Danvy","url":"https://www.semanticscholar.org/author/Olivier-Danvy/1705883"},{"name":"Henning Korsholm Rohde","url":"https://www.semanticscholar.org/author/Henning-Korsholm-Rohde/2469276"}],"venue":"ASIA-PEPM","year":2002,"stats":{},"journal":{"pages":"32-46"},"paperAbstract":"We present the first formal proof that partial evaluation of a quadratic string matcher can yield the precise behaviour of Knuth, Morris, and Pratt's linear string matcher.Obtaining a KMP-like string matcher is a canonical example of partial evaluation: starting from the naive, quadratic program checking whether a pattern occurs in a text, one ensures that backtracking can be performed at partial-evaluation time (a binding-time shift that yields a staged string matcher); specializing the resulting staged program yields residual programs that do not back up on the text, a la KMP. We are not aware, however, of any formal proof that partial evaluation of a staged string matcher precisely yields the KMP string matcher, or in fact any other specific string matcher.In this article, we present a staged string matcher and we formally prove that it performs the same sequence of comparisons between pattern and text as the KMP string matcher. To this end, we operationally specify each of the programming languages in which the matchers are written, and we formalize each sequence of comparisons with a trace semantics. We also state the (mild) conditions under which specializing the staged string matcher with respect to a pattern string provably yields a specialized string matcher whose size is proportional to the length of this pattern string and whose time complexity is proportional to the length of the text string. Finally, we show how tabulating one of the functions in this staged string matcher gives rise to the 'next' table of the original KMP algorithm.The method scales for obtaining other linear string matchers, be they known or new.","sourceIds":["conf/pepm/AgerDR02"]},{"url":"https://www.semanticscholar.org/paper/Mathematical-writing-by-Donald-E-Knuth-Tracy-Larra-Parsons/ed7cbe1b30eb520c9456ba63b3a668395ff93b82?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Mathematical writing by Donald E. Knuth, Tracy Larrabee and Paul M. Roberts, The Mathematical Association of America, 1989, 116pp, ISBN 0-88385-063-X","authors":[{"name":"Simon Parsons","url":"https://www.semanticscholar.org/author/Simon-Parsons/1678307"}],"venue":"Knowledge Eng. Review","year":1997,"stats":{},"journal":{"name":"Knowledge Eng. Review","volume":"12","pages":"331-334"},"sourceIds":["journals/ker/Parsons97a"]},{"url":"https://www.semanticscholar.org/paper/Book-Review-Stable-Marriage-and-its-Relation-to-Ot-McNicholl/3b3692cbf148e135a9cdf3d5a95ac7c4f487349b?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Book Review: Stable Marriage and its Relation to Other Combinatorial Problems: An Introduction to Algorithm Analysis by Donald E. Knuth (American Mathematical Society 1996)","authors":[{"name":"Timothy H. McNicholl","url":"https://www.semanticscholar.org/author/Timothy-H-McNicholl/1789626"}],"venue":"SIGACT News","year":1999,"stats":{},"journal":{"name":"SIGACT News","volume":"30","pages":"2-4"},"paperAbstract":"Welcome to the Book Reviews Column. We hope to bring you at least two reviews of books ever y month. In this column four books are reviewed. book uses the stable marriage problem as motivation to look at some mathematics of interest . It would be useful for undergrads ; however, for a serious study of matching there ar e more advanced and more up-to-date books available. 2. The Limits of Mathematics by Gregory J. Chaitin. Reviewed by Vladimir Tasic. Thi s book is on algorithmic information theory and randomness as they relate to Berr y's Parado x (\"the shortest number that requires less than 1000 characters to describe it\" has just bee n described by that phrase in quotes, yet that phrase was less than 1000 characters .) 3. Privacy on the Line by Whitfield Diffie and Susan Landau. Reviewed by Joseph Makle-vitch. This book is about the balance between the citizen's need for privacy and the govern-ment's need to intrude to prevent or solve crimes. These issues are relevant now because o f crytography and computers. The authors are respected theorists who have worked in cryptography , hence their comments are worthy considering. This book has caused some controvers y in the math community— see the June-July 1998 issue of Notices of the AMS, also available at http ://www.ams .org/notices. Or, better yet, read the book ! 4. A Theory of Objects by Authors : Martin Abadi and Luca Cardelli. Reviewed by Bria n Postow. This book is about formalizing the semantics of object-oriented languages. To d o this, a new calculus is introduced. 1 Overview This book is a translation of the revised and corrected edition of Marriages stables et leers relation s avec d'autres problemes combinatories published in 1976 by Les Presses de l'Universite de Montrea l. It is based on a series of lectures given by the author at the Centre de recherches mathematicques .","sourceIds":["journals/sigact/McNicholl99"]},{"url":"https://www.semanticscholar.org/paper/Digital-Typography-by-Donald-E-Knuth-CSLI-Publicat-Parsons/bec29c5ed6f5d53f62f5d21c7f04e49adfd8f091?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Digital Typography by Donald E. Knuth, CSLI Publications, 685 pp., US $89.95, ISBN 1-57586-010-4 and Pioneers of Modern Typography revised paperback edition by Herbert Spencer, MIT Press, 158 pp., US $29.95, ISBN 0-262-69303-8","authors":[{"name":"Simon Parsons","url":"https://www.semanticscholar.org/author/Simon-Parsons/1678307"}],"venue":"Knowledge Eng. Review","year":2004,"stats":{},"journal":{"name":"Knowledge Eng. Review","volume":"19","pages":"181-183"},"sourceIds":["journals/ker/Parsons04b"]},{"url":"https://www.semanticscholar.org/paper/A-review-of-Selected-Papers-on-Analysis-of-Algorit-McNicholl/dbf6df9d1cfa6aa91fb344f51688cc86600512e6?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"A review of Selected Papers on Analysis of Algorithms: by Donald E. Knuth","authors":[{"name":"Timothy H. McNicholl","url":"https://www.semanticscholar.org/author/Timothy-H-McNicholl/1789626"}],"venue":"SIGACT News","year":2001,"stats":{},"journal":{"name":"SIGACT News","volume":"32","pages":"5-8"},"paperAbstract":"it through the proofreading process...one naturally wonders what other mistakes may be lurking in the algorithms or code. The book takes a slightly abstract and general approach, defining abstract data types and then discussing particular specializations of them. While this approach is elegant, it may be problematic as an introductory approach for less theoretically-minded students. In the same vein, the book might benefit from using a more developmental approach to initial algorithm explanation (e.g. explaining a problem and then building up the solution in \"stream of consciousness\" step-by-step mode). (Of course, neither of these points necessarily apply to the reader who is mathematically sophisticated or who is reviewing previously-learned material, although for such readers other books such as Cormen et al's Introduction to Algorithms would be more suitable.) Data ,qtructure8 has a lot of good points, not least of which is a successful presentation of traditional data structures in an object-oriented framework; however, there are still some blemishes. If the authors put effort into incorporating feedback and increasing ease of understanding, the third edition could be a classic. Nevertheless, this second edition is quite usable as a classroom text or even as a reference for basic topics. This book contains an excellent collection of Donald Knuth's papers on the analysis of algorithm ,. In addition, there are a few papers on number theory. The chronological range of the essays begins with Knuth's first published paper on algorithm, in 1963 ('Analysis of Length of Strings in a Merge Sort') and continues until the present day ('Linear Probing and Graphs', 1998). The range of topics, although mostly confined to the analysis of algorithms, is vast. There are papers on game algorithms, algorithm, related to common mathematical problems (greatest common divisors , factoring, ...), and algorithms related to computer science problems. There are even a few philosophical and etymological essays. It is this wide range of topics that makes this a hard book to review. To focus on any one aspect of this book would give short-shrift to the others. I therefore decided to focus this review on w h y I believe e v e r y r e a d e r of S I G A C T n e w s should buy this book. I divided my reasons up into categories as follows. H i s t o r i c a l essays (the evolution of ...) …","sourceIds":["journals/sigact/McNicholl01"]},{"url":"https://www.semanticscholar.org/paper/The-art-of-computer-programming-Volume-III-2nd-Edi-Knuth/74d502b677abdc7c15a6925c3262cda0794cc3c9?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The art of computer programming, , Volume III, 2nd Edition","authors":[{"name":"Donald Ervin Knuth","url":"https://www.semanticscholar.org/author/Donald-Ervin-Knuth/10772633"}],"venue":"","year":1998,"stats":{"influentialCitations":10,"estimatedTotalCitations":{"min":185.37383748080103,"value":251.37383748080103,"max":341.37383748080106,"confidence":0.9}},"journal":{"pages":"I-XIII, 1-780"},"sourceIds":["books/lib/Knuth98a"]},{"url":"https://www.semanticscholar.org/paper/An-Empirical-Study-of-FORTRAN-Programs-Knuth/1a37d73677328521578b45cd47af43ff60096c39?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"An Empirical Study of FORTRAN Programs","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Softw., Pract. Exper.","year":1971,"stats":{"influentialCitations":6,"estimatedTotalCitations":{"min":298.3066260423859,"value":367.3066260423859,"max":456.3066260423859,"confidence":0.9}},"journal":{"name":"Softw., Pract. Exper.","volume":"1","pages":"105-133"},"sourceIds":["journals/spe/Knuth71"]},{"url":"https://www.semanticscholar.org/paper/The-Sandwich-Theorem-Knuth/80171441964f00a06642667434bcb34aace72da7?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Sandwich Theorem","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Electr. J. Comb.","year":1994,"stats":{"influentialCitations":3,"estimatedTotalCitations":{"min":194.37723317815608,"value":269.3772331781561,"max":371.3772331781561,"confidence":0.9}},"journal":{"name":"Electr. J. Comb.","volume":"1"},"paperAbstract":"This report contains expository notes about a function ti(G) that is popularly known as the Lovasz number of a graph G. There are many ways to define G(G), and the surprising variety of different characterizations indicates in itself that ti(G) should be interesting. But the most interesting property of 8(G) is probably the fact that it can be computed efficiently, although it lies \" sandwiched \" between other classic graph numbers whose computation is NP-hard. I have tried to make these notes self-contained so that they might serve as an elementary introduction to the growing literature on Lovasz's fascinating","sourceIds":["journals/combinatorics/Knuth94"]},{"url":"https://www.semanticscholar.org/paper/Dynamic-Huffman-Coding-Knuth/8dae04813f1005a31a84affe7158ff456eb880aa?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Dynamic Huffman Coding","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"J. Algorithms","year":1985,"stats":{"influentialCitations":5,"estimatedTotalCitations":{"min":227.16513376513672,"value":307.1651337651367,"max":414.1651337651367,"confidence":0.9}},"journal":{"name":"J. Algorithms","volume":"6","pages":"163-180"},"sourceIds":["journals/jal/Knuth85"]},{"url":"https://www.semanticscholar.org/paper/Randomized-Incremental-Construction-of-Delaunay-an-Guibas-Knuth/1b55521078461e591ea2a45da27d09234fabb978?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Randomized Incremental Construction of Delaunay and Voronoi Diagrams","authors":[{"name":"Leonidas J. Guibas","url":"https://www.semanticscholar.org/author/Leonidas-J-Guibas/1744254"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Micha Sharir","url":"https://www.semanticscholar.org/author/Micha-Sharir/1704273"}],"venue":"Algorithmica","year":1990,"stats":{"influentialCitations":3,"estimatedTotalCitations":{"min":405.2269944152224,"value":507.2269944152224,"max":634.2269944152224,"confidence":0.9}},"journal":{"pages":"414-431"},"sourceIds":["conf/icalp/GuibasKS90","journals/algorithmica/GuibasKS92"]},{"url":"https://www.semanticscholar.org/paper/Optimum-Binary-Search-Trees-Knuth/3762160cc38b5bf28cf76ebab12dfbde92c64243?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Optimum Binary Search Trees","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Acta Inf.","year":1971,"stats":{"influentialCitations":2,"estimatedTotalCitations":{"min":248.12429190304437,"value":324.12429190304437,"max":424.12429190304437,"confidence":0.9},"acceleration":{"min":0.0,"value":0.0,"max":0.0,"confidence":0.9}},"journal":{"name":"Acta Inf.","volume":"1","pages":"14-25"},"sourceIds":["journals/acta/Knuth71"]},{"url":"https://www.semanticscholar.org/paper/The-Problem-of-Compatible-Representatives-Knuth-Raghunathan/b06aaf536b4521dbae01995638097bbfc0e720d1?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Problem of Compatible Representatives","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Arvind Raghunathan","url":"https://www.semanticscholar.org/author/Arvind-Raghunathan/2468481"}],"venue":"SIAM J. Discrete Math.","year":1992,"stats":{"influentialCitations":2,"estimatedTotalCitations":{"min":90.2689053735763,"value":141.2689053735763,"max":219.2689053735763,"confidence":0.9}},"journal":{"name":"SIAM J. Discrete Math.","volume":"5","pages":"422-427"},"paperAbstract":"The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a rectangular map is NP-complete.","sourceIds":["journals/siamdm/KnuthR92"]},{"url":"https://www.semanticscholar.org/paper/Efficient-balanced-codes-Knuth/9152b63048150ed0a138291730cbe0f32b17fe20?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Efficient balanced codes","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"IEEE Trans. Information Theory","year":1986,"stats":{"influentialCitations":10,"estimatedTotalCitations":{"min":100.7414341154898,"value":142.7414341154898,"max":205.7414341154898,"confidence":0.9},"acceleration":{"min":0.07692307692307689,"value":0.0769230769230769,"max":0.07692307692307687,"confidence":0.9}},"journal":{"name":"IEEE Trans. Information Theory","volume":"32","pages":"51-53"},"paperAbstract":"Ahstruct-Coding schemes in which each codeword contains equally many zeros and ones are constructed in such a way that they can be efficiently encoded and decoded. A BINARY word of length m can be called balanced if it contains exactly lm/2] ones and [m/21 zeros. Let us say that a balanced code with n information bits and p parity bits is a set of 2 \" balanced binary words, each of length n + p. Balanced codes have the property that no codeword is \" contained \" in another; that is, the positions of the ones in one codeword will never be a subset of the positions of the ones in a different codeword. This property makes balanced codes attractive for certain applications, such as the encoding of unchangeable data on a laser disk [2]. Conversely , if we wish to form as many binary words of length m as possible with the property that no word is contained in another, Sperner's lemma [3] tells us that we can do no better than to construct the set of all balanced words of length m. A balanced code is efficient if there is a very simple way to encode and decode n-bit numbers. In other words, we want to find a one-to-one correspondence between the set of all n-bit binary words and the set of all (n + p)-bit codewords such that, if w corresponds to w', we can rapidly compute w' from w and vice versa. Furthermore, we want p to be very small compared with n, so that the code is efficient in its use of space as well as time. For example, it is trivial to construct a balanced code with n information bits and n parity bits by simply letting the binary word w correspond to the codeword w' = wW, where W is the complement of w. Encoding and decoding is clearly efficient in this case, but memory space is being wasted. Let M(m) = Imm/4 1) be the total number of balanced binary words of ength m. To have a balanced code with n information bits, we clearly need to have enough parity bits p so that M(n + p) 2 2 \". Stirling's approximation tells us that 1 44 logM(m)=m-ilogm-ilog:-m ' where 0 I c(m) 2 1.25/ln2 < 1.81; all logarithms here have radix 2, and the constant 1/21og p/2 is approximately 0.326. Therefore, …","sourceIds":["journals/tit/Knuth86"]},{"url":"https://www.semanticscholar.org/paper/Axioms-and-Hulls-Knuth/7203746aedee6bd4dcfa7064d77bbfde6a03ee79?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Axioms and Hulls","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Lecture Notes in Computer Science","year":1992,"stats":{"influentialCitations":3,"estimatedTotalCitations":{"min":120.83624625608661,"value":172.8362462560866,"max":248.8362462560866,"confidence":0.9}},"journal":{"volume":"606"},"sourceIds":["books/sp/Knuth92"]},{"url":"https://www.semanticscholar.org/paper/The-TeXbook-Knuth/4a57bd8f0b6fde980e9f63d2574eb41dbb659d4c?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The TeXbook","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"","year":1986,"stats":{"influentialCitations":5,"estimatedTotalCitations":{"min":79.27534852321276,"value":118.27534852321276,"max":179.27534852321276,"confidence":0.9}},"sourceIds":["books/aw/Knuth86"]},{"url":"https://www.semanticscholar.org/paper/Digital-Halftones-by-Dot-Diffusion-Knuth/01850e81ae46219abaed11ce458cf590ef0f16d7?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Digital Halftones by Dot Diffusion","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"ACM Trans. Graph.","year":1987,"stats":{"influentialCitations":2,"estimatedTotalCitations":{"min":171.23549033108966,"value":240.23549033108966,"max":337.23549033108964,"confidence":0.9}},"journal":{"name":"ACM Trans. Graph.","volume":"6","pages":"245-273"},"paperAbstract":"This paper describes a technique for approximating real-valued pixels by two-valued pixels. The new method, called dot diffusion, appears to avoid some deficiencies of other commonly used techniques. It requires approximately the same total number of arithmetic operations as the Floyd-Steinberg method of adaptive grayscale, and it is well suited to parallel computation; but it requires more buffers and more complex program logic than other methods when implemented sequentially. A “smooth” variant of the method may prove to be useful in high-resolution printing.","sourceIds":["journals/tog/Knuth87"]},{"url":"https://www.semanticscholar.org/paper/The-Errors-of-TEX-Knuth/ba50f608cdfd3568055f868fda5b67b93308fab0?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Errors of TEX","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Softw., Pract. Exper.","year":1989,"stats":{"influentialCitations":2,"estimatedTotalCitations":{"min":74.02084112588017,"value":115.02084112588017,"max":179.02084112588017,"confidence":0.9}},"journal":{"name":"Softw., Pract. Exper.","volume":"19","pages":"607-685"},"sourceIds":["journals/spe/Knuth89"]},{"url":"https://www.semanticscholar.org/paper/Breaking-Paragraphs-into-Lines-Knuth-Plass/ab4880923e457425ae027e083f97057d3491dbaf?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Breaking Paragraphs into Lines","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Michael F. Plass","url":"https://www.semanticscholar.org/author/Michael-F-Plass/3185485"}],"venue":"Softw., Pract. Exper.","year":1981,"stats":{"influentialCitations":1,"estimatedTotalCitations":{"min":124.56925359934999,"value":172.56925359935,"max":242.56925359935,"confidence":0.9}},"journal":{"name":"Softw., Pract. Exper.","volume":"11","pages":"1119-1184"},"sourceIds":["journals/spe/KnuthP81"]},{"url":"https://www.semanticscholar.org/paper/Mathematical-Analysis-of-Algorithms-Knuth/2a4a05e28b006f09fd0ba317f3ab1c5ed78df0c8?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Mathematical Analysis of Algorithms","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"IFIP Congress","year":1971,"stats":{"influentialCitations":3,"estimatedTotalCitations":{"min":142.46049442884,"value":196.46049442884,"max":273.46049442884,"confidence":0.9}},"journal":{"pages":"19-27"},"sourceIds":["conf/ifip/Knuth71"]},{"url":"https://www.semanticscholar.org/paper/A-Generalization-of-Dijkstra-s-Algorithm-Knuth/4771ee61809206700e8c3658f0e49448cf2037c5?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"A Generalization of Dijkstra's Algorithm","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Inf. Process. Lett.","year":1977,"stats":{"influentialCitations":5,"estimatedTotalCitations":{"min":129.21376310861777,"value":183.21376310861777,"max":261.21376310861774,"confidence":0.9}},"journal":{"name":"Inf. Process. Lett.","volume":"6","pages":"1-5"},"sourceIds":["journals/ipl/Knuth77"]},{"url":"https://www.semanticscholar.org/paper/Additional-comments-on-a-problem-in-concurrent-pro-Knuth/2bacdaead87a7b6582b148f9882e1073ea28feb3?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Additional comments on a problem in concurrent programming control","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Commun. ACM","year":1966,"stats":{"influentialCitations":1,"estimatedTotalCitations":{"min":97.77775886687016,"value":133.77775886687016,"max":187.77775886687016,"confidence":0.9}},"journal":{"name":"Commun. ACM","volume":"9","pages":"321-322"},"paperAbstract":"ment against the feature itself, if it is useful for other sound reasons. (b) The and proposal essentially is equivalent to Anderson's fork and join statements, although it assumes an entirely different form. It is all too obvious that the join and fork concepts emerged from their author's close familiarity with computer organization and machine code programming, and it is perhaps unfortunate for him to have chosen ALGOL as a vehicle to illustrate his ideas. The very essential innovation provided by ALGOL was structure; for example, repeated or conditional execution of a statement can be expressed by preceding it by a for clause or an if clause, instead of through use of several labels and jumps referenc-ing these labels. Therefore the fork and join statements using such labels are precisely contradictory to the fundamental principles on which ALGOL 60 is based. In case 2, where parallel execution is compulsory, the sharing of variables causes some problems, and Mr. Anderson's obtain and release statements are obviously intended to be used in this connection. Strictly speaking, however, they are not necessary, as has been denmnstrated by E. W. Dijkstra [3]. His \"critical sec-tions\" supposedly contain statements where individual computers access shared facilities, and through which they can communicate with each other. Although his algorithm does not seem to be entirely satisfactory (cf. [4]), the problem of eliminating interference is solved. In practical multiprocessor computers, an interlocking facility will probably be provided as a hardware feature, and it might be desirable that it be properly reflected in a programming language. From such a feature one would expect correct handling of the queueing problem, in the sense that the order in which requests occur be also the order in which access is granted [4]. A possible solution to the problem of accessing common variables or devices consistent with the philosophy of ALGOL, would be the awdlability of a special procedure declaration (e.g., a procedure declaration preceded by the symbol shared) written in a block surrounding all blocks representing the parallel programs. Any one program calling upon such a procedure would invoke the built-in queueing algorithm for this procedure (or \"critical sec-tion\") granting execution of that procedure only if all previously queued processors have terminated execution of that procedure. An example is given below.","sourceIds":["journals/cacm/Knuth66"]},{"url":"https://www.semanticscholar.org/paper/Computer-modern-typefaces-Knuth/611c8dcac227132e8d818c924957f523e9c9dddb?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Computer modern typefaces","authors":[{"name":"Donald Ervin Knuth","url":"https://www.semanticscholar.org/author/Donald-Ervin-Knuth/10772633"}],"venue":"","year":1986,"stats":{"influentialCitations":5,"estimatedTotalCitations":{"min":70.52018592415503,"value":90.52018592415503,"max":125.52018592415503,"confidence":0.9}},"journal":{"pages":"I-XV, 1-588"},"sourceIds":["books/lib/Knuth86a"]},{"url":"https://www.semanticscholar.org/paper/The-IBM-650-An-Appreciation-from-the-Field-Knuth/f9f11acf905858f53d8dd3ce7a1d61ced0ced127?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The IBM 650: An Appreciation from the Field","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Annals of the History of Computing","year":1986,"stats":{},"journal":{"name":"Annals of the History of Computing","volume":"8","pages":"50-55"},"paperAbstract":"How does one summarize the personal reminiscences of another of the giants in the computer field? Don Knuth is also an artist, of course, as witness his comments on Poley's code and his \" Art of Computer Programming. \" Knuth was a tremendous help to me in preparing this special issue. He wrote to other participants and encouraged them and me. Here is a letter he wrote me as this project was starting: When you asked if I might be interested in writing something about the IBM 650, I thought I might be able to come up with about two pages worth of stuff. But when I *began to reminisce, it became clear that I should write about ten times as much as I had originally thought. Here is the result; I hope you like it. Tears ran from my eyes as I (sob) wrote the conclusion! I suppose it was natural for a person like me to fall in how to use the wondrous card sorter. Meanwhile a love with his first computer. But there was something strange new machine had been installed across the special about the IBM 650, something that has pro-hall-it was what our student newspaper called \" an vided the inspiration for much of my life's work. IBM 650 Univac, \" or a \" giant brain. \" I was fascinated Somehow this machine was powerful in spite of its to look through the window and see the lights flashing severe limitations. Somehow it was friendly in spite on its console. of its primitive man-machine interface. One afternoon George Haynam explained some of I had just turned 19 when I was offered a part-time the machine's internal code to a bunch of us freshmen job helping the statisticians at Case Institute of Tech-who happened to be in the lab. It all sounded myste-nology. My first task was to draw graphs; but soon I rious to me, but it seemed to make a bit of sense, so I was given some keypunching duties, and I was taught got hold of a couple of manuals. My first chance to try the machine came a few weeks later, when one of Note: The preparation of this paper was supported in part by the-o~~~~-rr~~~ xi the fnakemt+q I w;~s-$ei!igi~e National Science Foundation grant MCS-83-00984. needed to know the five roots of a particular fifth-degree equation. I decided that it would …","sourceIds":["journals/annals/Knuth86"]},{"url":"https://www.semanticscholar.org/paper/A-Sequence-of-Series-for-the-Lambert-W-Function-Corless-Jeffrey/4b4b7b7b91d411de9d768f79ff1228b16c34eb82?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"A Sequence of Series for the Lambert W Function","authors":[{"name":"Robert M. Corless","url":"https://www.semanticscholar.org/author/Robert-M-Corless/2119294"},{"name":"David J. Jeffrey","url":"https://www.semanticscholar.org/author/David-J-Jeffrey/3350328"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"ISSAC","year":1997,"stats":{"influentialCitations":1,"estimatedTotalCitations":{"min":42.93738126384211,"value":76.93738126384211,"max":136.9373812638421,"confidence":0.9}},"journal":{"pages":"197-204"},"paperAbstract":"We give a uniform treatment of several series expansions for the Lambert W function, leading to an innnite family of new series. We also discuss standardization, complex branches, a family of arbitrary-order iterative methods for computation of W, and give a theorem showing how to correctly solve another simple and frequently occurring nonlinear equation in terms of W and the unwinding number.","sourceIds":["conf/issac/CorlessJK97"]},{"url":"https://www.semanticscholar.org/paper/Robert-W-Floyd-In-Memoriam-Knuth/407408b6522299dbd9692862580043e033da7070?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Robert W Floyd, In Memoriam","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"SIGACT News","year":2003,"stats":{},"journal":{"name":"SIGACT News","volume":"34","pages":"3-13"},"paperAbstract":"Nobody has influenced my scientific life more than Bob Floyd. Indeed, were it not for him, I might well have never become a computer scientist. In this note I'll try to explain some of the reasons behind these statements, and to capture some of the spirit of old-time computer science. Instead of trying to reconstruct the past using only incidents that I think I remember, I will quote extensively from actual documents that were written at the time things happened. The remarks below are extracted from a one-hour keynote speech I gave to the Stanford Computer Forum on 20 March 2002; many further details, including images of the original documents, can be seen in a video recording of that lecture, which has been permanently archived on the Internet by Stanford's Center for Professional Development [scpd.stanford.edu]. As in that lecture, I won't attempt to give a traditional biography, with balanced accounts of Bob's childhood, education, family life, career, and outside interests; I believe that the intriguing task of preparing such an account will be undertaken before long by professional historians who are much more qualified than I. My aim here is rather to present a personal perspective. My first encounter with Floyd's work goes back to 1962, when I was asked by Computing Reviews to assess his article \" A descriptive language for symbol manipulation \" [Journal of the Association for Computing Machinery 8 (1961), 579–584]. At that time I was studying mathematics as a second-year grad student at Caltech; he was working as a programmer-analyst at Armour Research Foundation in Chicago. Since I had recently completed a compiler for a subset of ALGOL, and had read the writeups and source listings of several other compilers, I was immediately impressed by what he had written [see Computing Reviews 3 (1962), 148, review #2140]: \" This paper is a significant step forward in the field of automatic programming. Over the past few years, simple algorithms for analyzing arithmetic expressions have been discovered independently by many people. But conventional methods for explaining such algorithms obscured the essential facts. Floyd has developed a new notation which lets the trees be distinguished from the forest, and which admirably points out what is really going on in a translation process. An algebraic compiler can be described very precisely and compactly in this notation, and one can design such a compiler in Floyd's form in a few …","sourceIds":["journals/sigact/Knuth03"]},{"url":"https://www.semanticscholar.org/paper/The-Joys-of-the-Asymptotics-Knuth/555e68a79ec95f5b6313a233222807fd8c427eca?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Joys of the Asymptotics","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"HERCMA","year":2001,"stats":{},"journal":{"pages":"1"},"sourceIds":["conf/hercma/Knuth01"]},{"url":"https://www.semanticscholar.org/paper/MMIXware-A-RISC-Computer-for-the-Third-Millennium-Knuth/cfe760b2d5d31ecdc28e9a9d8f4c9351545d7984?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"MMIXware, A RISC Computer for the Third Millennium","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Lecture Notes in Computer Science","year":1999,"stats":{},"journal":{"volume":"1750"},"sourceIds":["books/sp/Knuth99"]},{"url":"https://www.semanticscholar.org/paper/Efficient-Coroutine-Generation-of-Constrained-Gray-Knuth-Ruskey/27e0b34f8ca59463c5e5d0a6a7108f0895b830b2?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Efficient Coroutine Generation of Constrained Gray Sequences","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Frank Ruskey","url":"https://www.semanticscholar.org/author/Frank-Ruskey/1760415"}],"venue":"Essays in Memory of Ole-Johan Dahl","year":2004,"stats":{},"journal":{"pages":"183-208"},"paperAbstract":"We study an interesting family of cooperating coroutines, which is able to generate all patterns of bits that satisfy certain fairly general ordering constraints, changing only one bit at a time. (More precisely, the directed graph of constraints is required to be cycle-free when it is regarded as an undirected graph.) If the coroutines are implemented carefully, they yield an algorithm that needs only a bounded amount of computation per bit change, thereby solving an open problem in the field of combinatorial pattern generation. Much has been written about the transformation of procedures from recursive to iterative form, but little is known about the more general problem of transforming coroutines into equivalent programs that avoid unnecessary overhead. The present paper attempts to take a step in that direction by focusing on a reasonably simple yet nontrivial family of cooperating coroutines for which significant improvements in efficiency are possible when appropriate transformations are applied. The authors hope that this example will inspire other researchers to develop and explore the potentially rich field of coroutine transformation. Coroutines, originally introduced by M. E. Conway [2], are analogous to subroutines, but they are symmetrical with respect to caller and callee: When coroutine A invokes coroutine B, the action of A is temporarily suspended and the action of B resumes where B had most recently left off. Coroutines arise naturally in producer/consumer situations or multipass processes, analogous to the \" pipes \" of UNIX, when each coroutine transforms an input stream to an output stream; a sequence of such processes can be controlled in such a way that their intermediate data files need not be written in memory. (See, for example, Section 1.4.2 of [9].) The programming language SIMULA 67 [3] introduced support for coroutines in terms of fundamental operations named call, detach, and resume. Arne Wang and Ole-Johan Dahl subsequently discovered [20] that an extremely simple computational model is able to accommodate these primitive operations. Dahl published several examples to demonstrate their usefulness in his chapter of the book Structured Programming [4]; then M. Clint [1] and O.-J. Dahl [6] began to develop theoretical tools for formal proofs of coroutine cor-rectness. Another significant early work appeared in R. W. Floyd's general top-down parsing algorithm for context-free languages [8], an algorithm that involved \" imaginary men who are assumed to automatically appear when hired, disappear when fired, remember the names of their subordinates and superiors, …","sourceIds":["conf/birthday/KnuthR04"]},{"url":"https://www.semanticscholar.org/paper/Problem-10906-Knuth/7e189a0392fb42b6444470fcb2907d5321dac9fc?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Problem 10906","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2001,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"108","pages":"872"},"sourceIds":["journals/tamm/Knuth01c"]},{"url":"https://www.semanticscholar.org/paper/Problem-10985-Knuth/d03f74ce272d79a7d14bcd20edf5f0f67bd2839e?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Problem 10985","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"58"},"sourceIds":["journals/tamm/Knuth03"]},{"url":"https://www.semanticscholar.org/paper/Problem-10832-Knuth/6e4a46c88079c35e3acc89fdcc03ec252dbef3e8?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Problem 10832","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2000,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"107","pages":"863"},"sourceIds":["journals/tamm/Knuth00"]},{"url":"https://www.semanticscholar.org/paper/Recounting-the-Rationals-Continued-10906-Knuth-Rupert/11f767eba5cbb6b73b69dd18371221c42d490a81?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Recounting the Rationals, Continued: 10906","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"C. P. Rupert","url":"https://www.semanticscholar.org/author/C-P-Rupert/2383006"},{"name":"Alex Smith","url":"https://www.semanticscholar.org/author/Alex-Smith/9379592"},{"name":"Richard Stong","url":"https://www.semanticscholar.org/author/Richard-Stong/1747528"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"642-643"},"sourceIds":["journals/tamm/KnuthRSS03"]},{"url":"https://www.semanticscholar.org/paper/Exploring-All-Binary-Mazes-10720-Knuth-Lossers/8c19d93147bd433e001df23183d61ecd79a6a519?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Exploring All Binary Mazes: 10720","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"O. P. Lossers","url":"https://www.semanticscholar.org/author/O-P-Lossers/1782225"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"60-61"},"sourceIds":["journals/tamm/KnuthL03"]},{"url":"https://www.semanticscholar.org/paper/Fibonacci-in-Complex-Camouflage-10858-Knuth-Chapman/8358342fe250133d8b47185043b294e8f0c7188e?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Fibonacci in Complex Camouflage: 10858","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Robin J. Chapman","url":"https://www.semanticscholar.org/author/Robin-J-Chapman/4753686"}],"venue":"The American Mathematical Monthly","year":2004,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"111","pages":"166-167"},"sourceIds":["journals/tamm/KnuthC04"]},{"url":"https://www.semanticscholar.org/paper/Highly-Variable-Lists-10691-Knuth-Pedersen/899adfca6c77c5c035bf74946fe06cd8d66805ea?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Highly Variable Lists: 10691","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Allan Pedersen","url":"https://www.semanticscholar.org/author/Allan-Pedersen/11155643"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"59-60"},"sourceIds":["journals/tamm/KnuthP03"]},{"url":"https://www.semanticscholar.org/paper/Problem-11078-Knuth/8e7414c14c3ac4b6ad1250838a0c397d80926274?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Problem 11078","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2004,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"111","pages":"361"},"sourceIds":["journals/tamm/Knuth04"]},{"url":"https://www.semanticscholar.org/paper/Leaves-of-Ordered-Trees-10757-Kidwell-Knuth/780bb6c355bfe601ad68df45497b3cd0a3e473bc?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Leaves of Ordered Trees: 10757","authors":[{"name":"Mark E. Kidwell","url":"https://www.semanticscholar.org/author/Mark-E-Kidwell/3328206"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"O. P. Lossers","url":"https://www.semanticscholar.org/author/O-P-Lossers/1782225"}],"venue":"The American Mathematical Monthly","year":2001,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"108","pages":"874-875"},"sourceIds":["journals/tamm/KidwellKL01"]},{"url":"https://www.semanticscholar.org/paper/A-Fibonacci-Lucas-Extremum-10825-Miller-Knuth/c83f99c349751b05f55cc426c2b74df5ec97224b?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"A Fibonacci-Lucas Extremum: 10825","authors":[{"name":"Carl Miller","url":"https://www.semanticscholar.org/author/Carl-Miller/1988102"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2002,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"109","pages":"762-763"},"sourceIds":["journals/tamm/MillerK02"]},{"url":"https://www.semanticscholar.org/paper/Bottom-up-education-Knuth/8507c9d34d2c22bad3b90ef3a7e3ed4ba2d03c79?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Bottom-up education","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"ITiCSE","year":2003,"stats":{},"journal":{"pages":"2"},"paperAbstract":"People who discover the power and beauty of high-level, abstract ideas often make the mistake of believing that concrete ideas at lower levels are relatively worthless and might as well be forgotten. The speaker will argue that, on the contrary, the best computer scientists are thoroughly grounded in basic concepts of how computers actually work, and indeed that the essence of computer science is an ability to understand many levels of abstraction simultaneously. Therefore he has put considerable effort into the design of a RISC machine called MMIX, as an aid to computer science educators. MMIX is intended to be simple and clean yet realistic. Many tools have been built to simulate the MMIX architecture, and more are under development.","sourceIds":["conf/iticse/Knuth03"]},{"url":"https://www.semanticscholar.org/paper/Shellsort-with-three-increments-Janson-Knuth/022c4ee10cf69ef885888a39af9c6730ef8274e4?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Shellsort with three increments","authors":[{"name":"Svante Janson","url":"https://www.semanticscholar.org/author/Svante-Janson/1732375"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Random Struct. Algorithms","year":1997,"stats":{"influentialCitations":1},"journal":{"name":"Random Struct. Algorithms","volume":"10","pages":"125-142"},"paperAbstract":"A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments (h; g; 1). In particular, when h = (n 7=15) and g = (h 1=5), the average running time is O(n 23=15). The proof involves interesting properties of the inversions in random permutations that have been h-sorted and g-sorted. Shellsort, also known as the \\diminishing increment sort\" 7, Algorithm 5.2.1D], puts the elements of an array (X 0 ; : : : ; X n?1) into order by successively performing a straight insertion sort on larger and larger subarrays of equally spaced elements. The algorithm consists of t passes deened by increments (h t?1 ; : : : ; h 1 ; h 0), where h 0 = 1; the jth pass makes X k X l whenever l ? k = h t?j. A. C. Yao 11] has analyzed the average behavior of shellsort in the general three-pass case when the increments are (h; g; 1). The most interesting part of his analysis dealt with the third pass, where the running time is O(n) plus a term proportional to the average number of inversions that remain after a random permutation has been h-sorted and g-sorted. Yao proved that if g and h are relatively prime, the average number of inversions remaining is where the constant implied by b O depends on g and h. He gave a complicated triple sum for (h; g), which is too diicult to explain here; we will show that Moreover, we will prove that the average number of inversions after such h-sorting and g-sorting is The main technique used in proving (0.3) is to consider a stochastic algorithm A whose output has the same distribution as the inversions of the third pass of shellsort. Then by slightly perturbing the probabilities that deene A, we will obtain an algorithm A whose output has the expected value (h; g)n exactly. Finally we will prove that the perturbations cause the expected value to change by at most O(g 3 h 2). Section 1 introduces basic techniques for inversion counting, and section 2 adapts those techniques to a random input model. Section 3 proves that the crucial random variables needed for inversion counting are nearly uniform; then section 4 shows that the leading term (h; g)n in (0.3) would be exact if those variables were perfectly uniform. …","sourceIds":["journals/rsa/JansonK97"]},{"url":"https://www.semanticscholar.org/paper/The-Real-Numbers-Algebraically-10689-Knuth-Pratt/d8c264800e7b768c32d434214012d33e036cb115?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Real Numbers, Algebraically: 10689","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Vaughan R. Pratt","url":"https://www.semanticscholar.org/author/Vaughan-R-Pratt/1691192"},{"name":"O. P. Lossers","url":"https://www.semanticscholar.org/author/O-P-Lossers/1782225"}],"venue":"The American Mathematical Monthly","year":2000,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"107","pages":"755"},"sourceIds":["journals/tamm/KnuthPL00"]},{"url":"https://www.semanticscholar.org/paper/Some-Bernstein-Polynomials-10985-Knuth-al/e7851467e4950b07d7fbde0dc92d95332c59833b?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Some Bernstein Polynomials: 10985","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"et al.","url":"https://www.semanticscholar.org/author/et-al/1686612"}],"venue":"The American Mathematical Monthly","year":2004,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"111","pages":"447"},"sourceIds":["journals/tamm/Knutha04"]},{"url":"https://www.semanticscholar.org/paper/Problem-10913-Knuth/6ddddaf20a740768fa6af7c4d8c12b0d5fc611f6?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Problem 10913","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2001,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"108","pages":"977"},"sourceIds":["journals/tamm/Knuth01d"]},{"url":"https://www.semanticscholar.org/paper/Animals-in-a-Cage-10875-Knuth-Stong/bcde957683a149549e67f85a0bfa23d5b43390f4?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Animals in a Cage: 10875","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Richard Stong","url":"https://www.semanticscholar.org/author/Richard-Stong/1747528"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"243-245"},"sourceIds":["journals/tamm/KnuthS03"]},{"url":"https://www.semanticscholar.org/paper/The-Probability-of-Being-in-a-State-10726-Knuth-Stephenson/034eb9e63dc3bc59e9ce2e52ed646fb316150e41?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Probability of Being in a State: 10726","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Darin Stephenson","url":"https://www.semanticscholar.org/author/Darin-Stephenson/2531008"}],"venue":"The American Mathematical Monthly","year":2000,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"107","pages":"469-470"},"sourceIds":["journals/tamm/KnuthS00"]},{"url":"https://www.semanticscholar.org/paper/Balanced-Neighborhood-Squares-10871-Knuth-Carroll/fc7faa978bb4694f5f125e6138ae3766ca0ea8e3?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Balanced Neighborhood Squares: 10871","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Gabriel D. Carroll","url":"https://www.semanticscholar.org/author/Gabriel-D-Carroll/2163799"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"161-162"},"sourceIds":["journals/tamm/KnuthC03"]},{"url":"https://www.semanticscholar.org/paper/Products-of-Transpositions-10913-Knuth-Martin/e7da92b3b326781aee73a29a0b4ff15c73cccae7?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Products of Transpositions: 10913","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Reiner Martin","url":"https://www.semanticscholar.org/author/Reiner-Martin/2846339"}],"venue":"The American Mathematical Monthly","year":2003,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"110","pages":"844-845"},"sourceIds":["journals/tamm/KnuthM03"]},{"url":"https://www.semanticscholar.org/paper/The-Knowlton-Graham-Partition-Problem-Knuth/f498fd15a3c6f653dd3c37190c28220657d0d646?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"The Knowlton-Graham Partition Problem","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"J. Comb. Theory, Ser. A","year":1996,"stats":{},"journal":{"name":"J. Comb. Theory, Ser. A","volume":"73","pages":"185-189"},"paperAbstract":"A set partition technique that is useful for identifying wires in cables can be recast in the language of 0–1 matrices, thereby resolving an open problem stated by R. L. Graham in Volume 1 of this journal. The proof involves a construction of 0–1 matrices having row and column sums without gaps. A long cable contains n indistinguishable wires. Two people, one at each end, want to label the wires consistently so that both ends of each wire receive the same label. An interesting way to achieve this was proposed by K. C. to the condition that at most one element appears both in an A set of cardinality j and in a B set of cardinality k, for each j and k. We can then use the coordinates (j, k) to identify each element. R. L. Graham [2] proved that such partitioning schemes exist if and only if n = 2, 5, or 9. By restating the problem in terms of 0–1 matrices, it is possible to prove Graham's theorem more simply, and to sharpen the results of [2]. Lemma 1. Knowlton-Graham partitions for n exist if and only if there is a matrix of 0s and 1s having row sums n} with the Knowlton-Graham property , let a jk be the number of elements that appear in an A set of cardinality j and a B set of cardinality k. Then a jk is 0 or 1; and r j = k a jk is j times the number of A sets of cardinality j, while c k = j a jk is k times the number of B sets of cardinality k. Conversely, given such a matrix, we can use its rows to define A 1 ,. .. , A p such that each 1 in row j is in an A set of cardinality j; similarly its columns define B 1 ,. .. , B q such that each 1 in column k is in a B set of cardinality k. has row and column sums (2, 6, 3, 4, 5, 6) that satisfy the divisibility condition and sum to 26. To identify 26 wires, we can associate the 1s with arbitrary labels","sourceIds":["journals/jct/Knuth96"]},{"url":"https://www.semanticscholar.org/paper/Min-Plus-Matrix-Multiplication-10834-Kim-Johnsonbaugh/87b8cbf0191472750ccb7bebb7bea7145d5618cc?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Min-Plus Matrix Multiplication: 10834","authors":[{"name":"Sung Soo Kim","url":"https://www.semanticscholar.org/author/Sung-Soo-Kim/4434541"},{"name":"Richard Johnsonbaugh","url":"https://www.semanticscholar.org/author/Richard-Johnsonbaugh/13052202"},{"name":"Ronald E. Prather","url":"https://www.semanticscholar.org/author/Ronald-E-Prather/1812533"},{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2002,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"109","pages":"763-764"},"sourceIds":["journals/tamm/KimJPK02a","journals/tamm/KimJPK02"]},{"url":"https://www.semanticscholar.org/paper/Problem-10871-Knuth/af6bef969f4354e1ea85719f92ee3b10185b0f02?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Problem 10871","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"The American Mathematical Monthly","year":2001,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"108","pages":"372"},"sourceIds":["journals/tamm/Knuth01a"]},{"url":"https://www.semanticscholar.org/paper/Linear-Probing-and-Graphs-Knuth/69aad117b78a206f0a349bb5cddfeb86e6c8719a?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"Linear Probing and Graphs","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"Algorithmica","year":1998,"stats":{"influentialCitations":3},"journal":{"name":"Algorithmica","volume":"22","pages":"561-568"},"paperAbstract":"Mallows and Riordan showed in 1968 that labeled trees with a small number of inversions are related to labeled graphs that are connected and sparse. Wright enumerated sparse connected graphs in 1977, and Kreweras related the inversions of trees to the so-called \" parking problem \" in 1980. A combination of these three results leads to a surprisingly simple analysis of the behavior of hashing by linear probing, including higher moments of the cost of successful search. The well-known algorithm of linear probing for n items in m > n cells can be described as follows: Begin with all cells (0, 1,. .. , m − 1) empty; then for 1 ≤ k ≤ n, insert the kth item into the first nonempty cell in the sequence h k , (h k + 1) mod m, (h k + 2) mod m,. .. , where h k is a random integer in the range 0 ≤ h k < m. (See, for example, [4, Algorithm 6.4L].) The purpose of this note is to exhibit a surprisingly simple solution to a problem that appears in a recent book by Sedgewick and Flajolet [9]: Exercise 8.39 Use the symbolic method to derive the EGF of the number of probes required by linear probing in a successful search, for fixed M. The authors admitted that they did not know how to solve the problem, in spite of the fact that a \" symbolic method \" was the key to the analysis of all the other algorithms in their book. Indeed, the second moment of the distribution of successful search by linear probing was unknown when [9] was published in 1996. If the kth item is inserted into position q k , the quantity d = n k=1 (q k − h k) mod m is the total displacement of the items from their hash addresses. The average number of probes needed in a successful search is then 1 + d/n. Our goal in the following is to study the probability distribution of d as a function of the table size m and the number of items n.","sourceIds":["journals/algorithmica/Knuth98"]},{"url":"https://www.semanticscholar.org/paper/A-Stirling-Series-10832-Knuth-Rousseau/cc03e537a9edaea03bdaed59cf2b484b47291626?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"A Stirling Series: 10832","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"},{"name":"Cecil C. Rousseau","url":"https://www.semanticscholar.org/author/Cecil-C-Rousseau/2173520"}],"venue":"The American Mathematical Monthly","year":2001,"stats":{},"journal":{"name":"The American Mathematical Monthly","volume":"108","pages":"877-878"},"sourceIds":["journals/tamm/KnuthR01"]},{"url":"https://www.semanticscholar.org/paper/An-Exact-Analysis-of-Stable-Allocation-Knuth/6368e9d043cf7c6dc9a07df970837e6115efff46?utm_campaign=DBLP+Prototype&utm_source=DBLP&utm_medium=Partner+API","title":"An Exact Analysis of Stable Allocation","authors":[{"name":"Donald E. Knuth","url":"https://www.semanticscholar.org/author/Donald-E-Knuth/1717349"}],"venue":"J. Algorithms","year":1996,"stats":{"influentialCitations":3},"journal":{"name":"J. Algorithms","volume":"20","pages":"431-442"},"sourceIds":["journals/jal/Knuth96"]}],"total":2062}