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Let <italic>G=(V,E)</italic> be an undirected <italic>weighted</italic> graph with <italic>|V|=n</italic> and <italic>|E|=m</italic>. Let <italic>k\ge 1</italic> be an integer. We show that <italic>G=(V,E)</italic> can be preprocessed in <italic>O(kmn^{1/k})</italic> expected time, constructing a data structure of size <italic>O(kn^{1+1/k})</italic>, such(More)
We describe a novel randomized method, the method of color-coding for finding simple paths and cycles of a specified length k, and other small subgraphs, within a given graph G = (V,E). The randomized algorithms obtained using this method can be derandomized using families of perfect hash functions. Using the color-coding method we obtain, in particular,(More)
We describe several compact routing schemes for general weighted undirected networks. Our schemes are simple and easy to implement. The routing tables stored at the nodes of the network are all very small. The headers attached to the routed messages, including the name of the destination, are extremely short. The routing decision at each node takes(More)
Reachability and distance queries in graphs are fundamental to numerous applications, ranging from geographic navigation systems to Internet routing. Some of these applications involve huge graphs and yet require fast query answering. We propose a new data structure for representing all distances in a graph. The data structure is <i>distributed</i> in the(More)
We study the complexity of nding the values and optimal strategies of mean payoo games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudo-polynomial time algorithm for the solution of such games, the decision problem for which is in NP \ co-NP.(More)
  • Uri Zwick
  • Electronic Colloquium on Computational Complexity
  • 2000
We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms.The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in <i>&#213;</i>(<i>n</i><sup>2+&mu;</sup>) time,(More)
We describe a randomized approximation algorithm which takes an instance of MAX 3SAT as input. If the instance—a collection of clauses each of length at most three—is satisfiable, then the expected weight of the assignment found is at least 7=8 of optimal. We provide strong evidence (but not a proof) that the algorithm performs equally well on arbitrary MAX(More)
Let G = (V;E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of Aingworth, Chekuri and Motwani, we describe an ~ O(minfn3=2m1=2; n7=3g) time algorithmAPASP2 for computing all distances(More)