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How to represent a graph in memory is a fundamental data structuring question. In the usual representations of an <italic>n</italic>-node graph, the names of the nodes (i.e. integers from 1 to <italic>n</italic>) betray nothing about the graph itself. Indeed, the names (or labels) on the <italic>n</italic> nodes are just log<italic>n</italic> bit place… (More)

We formalize a potentially rich new streaming model, the semi-streaming model, that we believe is necessary for the fruitful study of efficient algorithms for solving problems on massive graphs whose edge sets cannot be stored in memory. In this model, the input graph, G = (V, E), is presented as a stream of edges (in adversarial order), and the storage… (More)

A <italic>program correctness checker</italic> is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It designs program checkers for a few specific… (More)

We extend the notion of program checking to include programs which alter their environment. In particular, we consider programs which store and retrieve data from memory. The model we consider allows the checker a small amount of reliable memory. The checker is presented with a sequence of requests (on-line) to a data structure which must reside in a large… (More)

We investigate the importance of space when solving problems based on graph distance in the streaming model. In this model, the input graph is presented as a stream of edges in an arbitrary order. The main computational restriction of the model is that we have limited space and therefore cannot store all the streamed data; we are forced to make… (More)

A new method that simultaneously aligns and reconstructs ancestral sequences for any number of homologous sequences, when the phylogeny is given, Mol. Biol. Evol. 6(6):649-668m 1989. [22] J. Hein, A tree reconstruction method that is economical in the number of pairwise comparisons used, Mol. { 23 { We examined the methods by which biologists actually… (More)

We give a space-efficient, one-pass algorithm for approximating the L 1 difference P i ja i ? b i j between two functions , when the function values a i and b i are given as data streams, and their order is chosen by an adversary. Our main technical innovation is a method of constructing families fV j g of limited-independence random variables that are… (More)

A quasi-polynomial-time algorithm is presented for sampling almost uniformly at random from the n-slice of the language L(G) generated by an arbitrary context-free grammar G. (The n-slice of a language L over an alphabet is the subset L\ n of words of length exactly n.) The time complexity of the algorithm is " ?2 (n jGj) O(log n) , where the parameter "… (More)

Isotonic regression, the problem of finding values that best fit given observations and conform to specific ordering constraints, has found many applications in biomedical research and other fields. When the constraints form a partial ordering, solving the problem under the L1 error measure takes O(n 3) when there are n observations. The analysis of… (More)

We describe a procedure which may be helpful to any disorganized carpenter who has a mixed pile of bolts and nuts and wants to nd the corresponding pairs of bolts and nuts. The procedure uses our (and the carpenter's) ability to construct eeciently highly expanding graphs. The problem considered is given a collection of n bolts of distinct widths and n nuts… (More)