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- W2895866428 abstract "We consider the problem of computing all pairs shortest paths (APSP) and shortest paths for k sources in a weighted graph in the distributed CONGEST model. For graphs with non-negative integer edge weights (including zero weights) we build on a recent pipelined algorithm to obtain $tilde{O}(lambda^{1/4}cdot n^{5/4})$ in graphs with non-negative integer edge-weight at most $lambda$, and $tilde{O}(n cdot bigtriangleup^{1/3})$ rounds for shortest path distances at most $bigtriangleup$. Additionally, we simplify some of the procedures in the earlier APSP algorithms for non-negative edge weights in [HNS17,ARKP18]. We also present results for computing h-hop shortest paths and shortest paths from $k$ given sources. In other results, we present a randomized exact APSP algorithm for graphs with arbitrary edge weights that runs in $tilde{O}(n^{4/3})$ rounds w.h.p. in n, which improves the previous best $tilde{O}(n^{3/2})$ bound, which is deterministic. We also present an $tilde{O}(n/epsilon^2)$-round deterministic $(1+epsilon)$ approximation algorithm for graphs with non-negative $poly(n)$ integer weights (including zero edge-weights), improving results in [Nanongkai14,LP15] that hold only for positive integer weights." @default.
- W2895866428 created "2018-10-26" @default.
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- W2895866428 date "2018-10-18" @default.
- W2895866428 modified "2023-09-27" @default.
- W2895866428 title "New and Simplified Distributed Algorithms for Weighted All Pairs Shortest Paths." @default.
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