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- W2746769191 abstract "We study computing {em all-pairs shortest paths} (APSP) on distributed networks (the CONGEST model). The goal is for every node in the (weighted) network to know the distance from every other node using communication. The problem admits $(1+o(1))$-approximation $tilde O(n)$-time algorithms ~cite{LenzenP-podc15,Nanongkai-STOC14}, which are matched with $tilde Omega(n)$-time lower bounds~cite{Nanongkai-STOC14,LenzenP_stoc13,FrischknechtHW12}footnote{$tilde Theta$, $tilde O$ and $tilde Omega$ hide polylogarithmic factors. Note that the lower bounds also hold even in the unweighted case and in the weighted case with polynomial approximation ratios.}. No $omega(n)$ lower bound or $o(m)$ upper bound were known for exact computation. In this paper, we present an $tilde O(n^{5/4})$-time randomized (Las Vegas) algorithm for exact weighted APSP; this provides the first improvement over the naive $O(m)$-time algorithm when the network is not so sparse. Our result also holds for the case where edge weights are {em asymmetric} (a.k.a. the directed case where communication is bidirectional). Our techniques also yield an $tilde O(n^{3/4}k^{1/2}+n)$-time algorithm for the {em $k$-source shortest paths} problem where we want every node to know distances from $k$ sources; this improves Elkin's recent bound~cite{Elkin-STOC17} when $k=tilde omega(n^{1/4})$." @default.
- W2746769191 created "2017-08-31" @default.
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- W2746769191 date "2017-08-13" @default.
- W2746769191 modified "2023-10-07" @default.
- W2746769191 title "Distributed Exact Weighted All-Pairs Shortest Paths in $tilde O(n^{5/4})$ Rounds" @default.
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