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Computer Science > Data Structures and Algorithms

arXiv:2203.03456 (cs)
[Submitted on 7 Mar 2022 (v1), last revised 30 Oct 2022 (this
version, v4)]

Title:Negative-Weight Single-Source Shortest Paths in Near-linear
Time

Authors:Aaron Bernstein, Danupon Nanongkai, Christian Wulff-Nilsen
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    Abstract: 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].

Comments: Simplified algorithm for Low-Diameter Decomposition and
          minor corrections
Subjects: Data Structures and Algorithms (cs.DS)
Cite as:  arXiv:2203.03456 [cs.DS]
          (or arXiv:2203.03456v4 [cs.DS] for this version)
          https://doi.org/10.48550/arXiv.2203.03456
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Danupon Nanongkai [view email]
[v1] Mon, 7 Mar 2022 15:15:09 UTC (51 KB)
[v2] Tue, 5 Apr 2022 08:34:33 UTC (48 KB)
[v3] Sun, 8 May 2022 12:50:44 UTC (44 KB)
[v4] Sun, 30 Oct 2022 05:54:26 UTC (57 KB)
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