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- W3044798784 abstract "We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph $G=(V, E)$ with edge weights in ${1, 2, dots, M}$, we need to preprocess it into a data structure, and answer the following queries: given vertices $u,vin V$ and a failed vertex or edge $fin (Vcup E)$, output the length of the shortest path from $u$ to $v$ that does not go through $f$. Our main result is a simple DSO with $tilde{O}(n^{2.7233}M)$ preprocessing time and $O(1)$ query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to $tilde{O}(n^{2.6865}M)$. The preprocessing algorithm is randomized with correct probability $ge 1-1/n^C$, for a constant $C$ that can be made arbitrarily large. Previously, there is a DSO with $tilde{O}(n^{2.8729}M)$ preprocessing time and $operatorname{polylog}(n)$ query time [Chechik and Cohen, STOC'20]. At the core of our DSO is the following observation from [Bernstein and Karger, STOC'09]: if there is a DSO with preprocessing time $P$ and query time $Q$, then we can construct a DSO with preprocessing time $P+tilde{O}(n^2)cdot Q$ and query time $O(1)$. (Here $tilde{O}(cdot)$ hides $operatorname{polylog}(n)$ factors.)" @default.
- W3044798784 created "2020-07-29" @default.
- W3044798784 creator A5070520262 @default.
- W3044798784 date "2020-07-22" @default.
- W3044798784 modified "2023-10-16" @default.
- W3044798784 title "Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time" @default.
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- W3044798784 doi "https://doi.org/10.48550/arxiv.2007.11495" @default.
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