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• W4313227229 abstract "We present a randomized algorithm that computes single-source shortest paths (SSSP) in $Oleft(m log ^{8}(n) log Wright)$ time when edge weights are integral and can be negative. <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> This essentially resolves the classic negative-weight SSSP problem. The previous bounds are $tilde{O}left(left(m+n^{1.5}right) log Wright)$ [BLNPSSSW FOCS’20] and $m^{4 / 3+o(1)} log W$ [AMV FOCS’20]. Near-linear time algorithms were known previously only for the special case of planar directed graphs [Fakcharoenphol and Rao FOCS’01]. In contrast to all recent developments that rely on sophisticated continuous optimization methods and dynamic algorithms, our algorithm is simple: it requires only a simple graph decomposition and elementary combinatorial tools. In fact, ours is the first combinatorial algorithm for negative-weight SSSP to break through the classic $O(m sqrt{n} log W)$ bound from over three decades ago [Gabow and Tarjan SICOMP’89]." @default.
• W4313227229 created "2023-01-06" @default.
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• W4313227229 date "2022-10-01" @default.
• W4313227229 modified "2023-10-12" @default.
• W4313227229 title "Negative-Weight Single-Source Shortest Paths in Near-linear Time" @default.
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• W4313227229 doi "https://doi.org/10.1109/focs54457.2022.00063" @default.
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