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- W4288281011 abstract "In the sensitive distance oracle problem, there are three phases. We first preprocess a given directed graph $G$ with $n$ nodes and integer weights from $[-W,W]$. Second, given a single batch of $f$ edge insertions and deletions, we update the data structure. Third, given a query pair of nodes $(u,v)$, return the distance from $u$ to $v$. In the easier problem called sensitive reachability oracle problem, we only ask if there exists a directed path from $u$ to $v$. Our first result is a sensitive distance oracle with $tilde{O}(Wn^{omega+(3-omega)mu})$ preprocessing time, $tilde{O}(Wn^{2-mu}f^{2}+Wnf^{omega})$ update time, and $tilde{O}(Wn^{2-mu}f+Wnf^{2})$ query time where the parameter $muin[0,1]$ can be chosen. The data-structure requires $O(Wn^{2+mu} log n)$ bits of memory. This is the first algorithm that can handle $fgelog n$ updates. Previous results (e.g. [Demetrescu et al. SICOMP'08; Bernstein and Karger SODA'08 and FOCS'09; Duan and Pettie SODA'09; Grandoni and Williams FOCS'12]) can handle at most 2 updates. When $3le flelog n$, the only non-trivial algorithm was by [Weimann and Yuster FOCS'10]. When $W=tilde{O}(1)$, our algorithm simultaneously improves their preprocessing time, update time, and query time. In particular, when $f=omega(1)$, their update and query time is $Omega(n^{2-o(1)})$, while our update and query time are truly subquadratic in $n$, i.e., ours is faster by a polynomial factor of $n$. To highlight the technique, ours is the first graph algorithm that exploits the kernel basis decomposition of polynomial matrices by [Jeannerod and Villard J.Comp'05; Zhou, Labahn and Storjohann J.Comp'15] developed in the symbolic computation community. [...]" @default.
- W4288281011 created "2022-07-28" @default.
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- W4288281011 date "2019-07-18" @default.
- W4288281011 modified "2023-09-29" @default.
- W4288281011 title "Sensitive Distance and Reachability Oracles for Large Batch Updates" @default.
- W4288281011 doi "https://doi.org/10.48550/arxiv.1907.07982" @default.
- W4288281011 hasPublicationYear "2019" @default.
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