Big Omicron and big Omega and big Theta

  title={Big Omicron and big Omega and big Theta},
  author={Donald Ervin Knuth},
  journal={SIGACT News},
  • D. Knuth
  • Published 1 April 1976
  • Education
  • SIGACT News
Most of us have gotten accustomed to the idea of using the notation O(f(n)) to stand for any function whose magnitude is upper-bounded by a constant times f(n) , for all large n. Sometimes we also need a corresponding notation for lower-bounded functions, i.e., those functions which are at least as large as a constant times f(n) for all large n. Unfortunately~ people have occasionally been using the O-notation for lower bounds, for example when they reject a particular sorting method "because… 
What does O(n) mean
The traditional notation is defended here, despite the fact that the new notation calls for extending arithmetic operations from functions to sets of functions, and gives rise, as Gilles Brassard honestly and immediately acknowledges, to a new type of ambiguous expressions.
The Big-O of Mathematics and Computer Science
  • F. Mala, Rouf Ali
  • Computer Science
    Journal of Applied Mathematics and Computation
  • 2022
It is shown, using examples, how the Big-O notation could turn out to be a better, easier and more informative notation compared to the limit notation of a function.
Topics of Mathematics in Cryptology Asymptotic Notation
And now you ask: What is the running time of the main program in terms of n? Given the above, this is difficult to answer. f(a) makes a2 multiplications. How much time does a multiplication take?
Two decades of applied Kolmogorov complexity: in memoriam Andrei Nikolaevich Kolmogorov 1903-87
  • Ming Li, P. Vitányi
  • Computer Science
    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
The authors provide an introduction to the main ideas of Kolmogorov complexity and survey the wealth of useful applications of this notion. It is based on a theory of information content of strings,
Crusade for a better notation
In a well-known SIGACT/NEWS paper, Knuth sets forth the asymptotic notation by which the authors all now live and proposes that members of SIGACT adopt the O, Ω and Θ notations unless a better alternative can be found reasonably soon.
TME Volume 13, Number 3
The decimal expansions of the numbers 1{n (such as 1{3 “ 0.3333..., 1{7 “ 0.142857...) are most often viewed as tools for approximating quantities to a desired degree of accuracy. The aim of this
Series misdemeanors
Issues such as avoiding unnecessary restrictions such as prohibiting negative or fractional requested orders, the pros and cons of displaying results with explicit infectious error terms, efficient data structures, and algorithms that efficiently give users exactly the order or number of nonzero terms they request are discussed.
Foreword This chapter is based on lecture notes from coding theory courses taught by Venkatesan
1. Asymptotics of codes: Given > 0 express the rate of the best family of binary codes of relative distance 1 2 − , you can (a) construct, and (b) show the existence of. Express the rate in big-Oh
Teaching Algorithms and Data Structures: 10 Personal Observations
  • H. Bieri
  • Education
    Computer Science in Perspective
  • 2003
The elementary textbooks on algorithms and data structures have become too canonical too quickly, and that certain ways of presentation and also of selecting the contents are not as justified as they seem to be.
Remarks on Abstracto
High-level programming languages have had a direct influence on the presentation of algorithms in the literature and many an author now employs a kind of pidgin ALGOL to express himself.


An Algorithm for the Computation of Linear Forms
An algorithm is presented here which implies that every polynomial of degree n with at most s distinct coefficients can be realized with O(n/\log _s n) operations.
Some problems of diophantine approximation
Let 0 be an irrational number, and a any number between 0 and 1 (0 included). Then it is well known that it is possible to find a sequence of positive integers w<i, n2, n3, ... such that (nr0) —>a as
Die Analytische Zahlentheorie. Zahlentheorie, pt
  • Die Analytische Zahlentheorie. Zahlentheorie, pt
Leipzig: B. G. Teubner
  • Leipzig: B. G. Teubner
  • 1894
Savage presents therein a generalization of the Four Russians' Algorithm, several applications of it, and a counting argument lower bound similar to Moon and Moser's. Sincerely
  • Savage presents therein a generalization of the Four Russians' Algorithm, several applications of it, and a counting argument lower bound similar to Moon and Moser's. Sincerely
II May
  • II May
  • 1976