Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing - STOC '92 1992
DOI: 10.1145/129712.129785
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A parallel randomized approximation scheme for shortest paths

Abstract: We give a randomized parallel algorithm for approximate shortest path computation in an undirected weight ed graph. The algorithm is based on a technique used by Unman and Yannakakis in a parallel algorithm for breadth-first search. It has application, e.g., in approximate solution of multi commodit y flow problems with unit capacities. We also show how to adapt the algorithm to perform better for planar graphs.

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Cited by 27 publications
(12 citation statements)
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“…Klein [20] extended the work of Ullman and Yannakakis [27] to the weighted case, obtaining a randomized PRAM algorithm that can (1 + )-approximate shortest paths between k pairs of vertices in O( √ n −2 log n · log * n) time using (kE log n) 2 processors (where is constant). When this algorithm is run sequentially, the time is not as good as known sequential algorithms for the exact problem.…”
Section: 1mentioning
confidence: 99%
“…Klein [20] extended the work of Ullman and Yannakakis [27] to the weighted case, obtaining a randomized PRAM algorithm that can (1 + )-approximate shortest paths between k pairs of vertices in O( √ n −2 log n · log * n) time using (kE log n) 2 processors (where is constant). When this algorithm is run sequentially, the time is not as good as known sequential algorithms for the exact problem.…”
Section: 1mentioning
confidence: 99%
“…The work performed depends on the size of the cover. To achieve an efficient parallel construction of pairwise covers, we refine the definition to be with respect to an additional "path size" parameter C. For a parameter 1 5 C 5 n , the C-limited distance between a pair of vertices is the weight of the minimum-weight path connecting them among paths consisting of at most C edges (this terminology is from [7]). In pairwise covers with parameter e, we have a relaxed requirement that pairs of vertices where the !-limited distance between them is a t most W must be both contained in at least one cluster.…”
Section: Overviewmentioning
confidence: 99%
“…The weights U, are obtained by scaling and rounding up the weights w . The reduction is based on a technique and ideas from Klein and Sairam [7]. ...…”
Section: Computing An (E P W ;)-Covermentioning
confidence: 99%
“…The basic sparsification technique works best with paths that are all roughly of same length. To accommodate this, we use a grouping technique (see, e.g., [14]). …”
Section: 2mentioning
confidence: 99%