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• W3131153721 abstract "Consider an undirected weighted graph $G = (V,E,w)$. We study the problem of computing $(1+epsilon)$-approximate shortest paths for $S times V$, for a subset $S subseteq V$ of $|S| = n^r$ sources, for some $0 0$. In particular, for $r le 0.313ldots$, our centralized algorithm computes $S times V$ $(1+epsilon)$-approximate shortest paths in $n^{2 + o(1)}$ time. Our PRAM polylogarithmic-time algorithm has work complexity $O(|E| cdot n^rho + n^{2+o(1)})$, for any arbitrarily small constant $rho >0$. Previously existing solutions either require centralized time/parallel work of $O(|E| cdot |S|)$ or provide much weaker approximation guarantees. In the Congested Clique model, our algorithm solves the problem in polylogarithmic time for $|S| = n^r$ sources, for $r le 0.655$, while previous state-of-the-art algorithms did so only for $r le 1/2$. Moreover, it improves previous bounds for all $r > 1/2$. For unweighted graphs, the running time is improved further to $poly(loglog n)$." @default.
• W3131153721 created "2021-03-01" @default.
• W3131153721 creator A5066182501 @default.
• W3131153721 creator A5075683085 @default.
• W3131153721 date "2020-04-16" @default.
• W3131153721 modified "2023-09-27" @default.
• W3131153721 title "Centralized, Parallel, and Distributed Multi-Source Shortest Paths via Hopsets and Rectangular Matrix Multiplication" @default.
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• W3131153721 hasPublicationYear "2020" @default.
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