Proceedings ArticleDOI
Parallel depth-first search in general directed graphs
Alok Aggarwal,Richard J. Anderson,Ming-Yang Kao +2 more
- pp 297-308
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In this article, it was shown that the problem of finding a directed cycle separator is in randomized NC and also proved that computing cycle separators and conducting depth-first search in directed graphs are deterministic NC-equivalent.Abstract:
A directed cycle separator of an n-vertex directed graph is a simple directed cycle such that when the vertices of the cycle are deleted, the resulting graph has no strongly connected component with more than n/2 vertices. This paper shows that the problem of finding a directed cycle separator is in randomized NC. The paper also proves that computing cycle separators and conducting depth-first search in directed graphs are deterministic NC-equivalent. These two results together yield the first RNC algorithm for depth-first search in directed graphs.read more
Citations
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Proceedings ArticleDOI
Graph-theoretic methods in database theory
TL;DR: This work will concentrate on a particular, basic type of problems that has attracted a great deal of attention in the database literature over the last few years and has come to play a central role: techniques for searching graphs and computing transitive closure, and some of the applications and related problems in query processing.
Book ChapterDOI
On Identifying Strongly Connected Components in Parallel
TL;DR: For a graph with n vertices in which degrees are bounded by a constant, the expected serial running time of their algorithm was O(n log n) as discussed by the authors, where n is the number of vertices.
Proceedings ArticleDOI
Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable
TL;DR: It is shown that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes.
Journal ArticleDOI
Connected Components inO(log3/2n) Parallel Time for the CREW PRAM
TL;DR: This work presents a simple algorithm that runs inO(log3/2n) time usingn+mCREW processors, and simulates this algorithm on the weaker CREW model increases its running time to O(log2n).
Posted Content
Bipartite Perfect Matching is in quasi-NC
TL;DR: In this paper, it was shown that the bipartite perfect matching problem is in quasi-NC$^2 and has uniform circuits of quasi-polynomial size with polylogarithmic depth.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Proceedings ArticleDOI
Matrix multiplication via arithmetic progressions
Don Coppersmith,Shmuel Winograd +1 more
TL;DR: A new method for accelerating matrix multiplication asymptotically is presented, by using a basic trilinear form which is not a matrix product, and making novel use of the Salem-Spencer Theorem.
Proceedings ArticleDOI
Matching is as easy as matrix inversion
TL;DR: A new algorithm for finding a maximum matching in a general graph that its only computationally non-trivial step is the inversion of a single integer matrix, the isolating lemma, and other applications to parallel computation and randomized reductions are shown.
Journal ArticleDOI
Matching is as easy as matrix inversion
TL;DR: A new algorithm for finding a maximum matching in a general graph with special feature is that its only computationally non-trivial step is the inversion of a single integer matrix, the isolating lemma.
Journal ArticleDOI
Depth-first search is inherently sequential
TL;DR: It is shown that this problem, for undirected and directed graphs, is complete in deterministic polynomial time with respect to deterministic log-space reductions.