Negative-Weight Single-Source Shortest Paths in Near-linear Time
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909616132063232 |
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| author | Bernstein, Aaron Nanongkai, Danupon Wulff-Nilsen, Christian |
| author_facet | Bernstein, Aaron Nanongkai, Danupon Wulff-Nilsen, Christian |
| contents | We present a randomized algorithm that computes single-source shortest paths (SSSP) in $O(m\log^8(n)\log W)$ time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are $\tilde O((m+n^{1.5})\log W)$ [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 $\tilde O(m\sqrt{n}\log W)$ bound from over three decades ago [Gabow and Tarjan SICOMP'89]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_03456 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Negative-Weight Single-Source Shortest Paths in Near-linear Time Bernstein, Aaron Nanongkai, Danupon Wulff-Nilsen, Christian Data Structures and Algorithms We present a randomized algorithm that computes single-source shortest paths (SSSP) in $O(m\log^8(n)\log W)$ time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are $\tilde O((m+n^{1.5})\log W)$ [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 $\tilde O(m\sqrt{n}\log W)$ bound from over three decades ago [Gabow and Tarjan SICOMP'89]. |
| title | Negative-Weight Single-Source Shortest Paths in Near-linear Time |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2203.03456 |