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We give a randomized parallel algorithm for approximate shortest path computation in an undirected weighted graph. The algorithm is based on a technique used by Ullman and Yannakakis in a parallel algorithm for breadth-first search. It has application, e.g., in approximate solution of multicommodity flow problems with unit capacities. We also show how to… (More)

Computing shortest paths in a directed graph has received considerable attention in the sequential RAM model of computation. However, developing a polylog-time parallel algorithm that is close to the sequential optimal in terms of the total work done remains an elusive goal. We present a rst step in this direction by showing that for an n-node planar… (More)

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