TY - GEN

T1 - Negative-Weight Single-Source Shortest Paths in Near-linear Time

AU - Bernstein, Aaron

AU - Nanongkai, Danupon

AU - Wulff-Nilsen, Christian

PY - 2022

Y1 - 2022

N2 - We present a randomized algorithm that computes single-source shortest paths (SSSP) in O(mlog(8)(n) logW) time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are (O) over tilde ((m + n(1.5)) logW) [BLNPSSSW FOCS'20] and m(4/3+o(1)) logW [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) over tilde (m root n logW) bound from over three decades ago [Gabow and Tarjan SICOMP'89].

AB - We present a randomized algorithm that computes single-source shortest paths (SSSP) in O(mlog(8)(n) logW) time when edge weights are integral and can be negative. This essentially resolves the classic negative-weight SSSP problem. The previous bounds are (O) over tilde ((m + n(1.5)) logW) [BLNPSSSW FOCS'20] and m(4/3+o(1)) logW [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) over tilde (m root n logW) bound from over three decades ago [Gabow and Tarjan SICOMP'89].

KW - graphs and networks

KW - path and circuit problems

KW - graph algorithms

KW - analysis of algorithms

KW - SCALING ALGORITHMS

KW - GRAPHS

U2 - 10.1109/FOCS54457.2022.00063

DO - 10.1109/FOCS54457.2022.00063

M3 - Article in proceedings

T3 - Annual IEEE Symposium on Foundations of Computer Science

SP - 600

EP - 611

BT - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)

PB - IEEE

T2 - 63rd Annual IEEE Symposium on Foundations of Computer Science (FOCS)

Y2 - 31 October 2022 through 3 November 2022

ER -