All-Pairs shortest paths in o(n2) time with high probability

Yuval Peres, Dmitry Sotnikov, Benny Sudakov, Uri Zwick

Research output: Contribution to journalArticlepeer-review

Abstract

We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0, 1] is O(n2), in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]. The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n2), in expectation and with high probability. We also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in O(log2 n) expected time.

Original languageEnglish
Article number26
JournalJournal of the ACM
Volume60
Issue number4
DOIs
StatePublished - Aug 2013

Keywords

  • Probabilistic analysis
  • Shortest paths

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