All-pairs shortest paths in O(n2) time with high probability

Yuval Peres, Dmitry Sotnikov, Benny Sudakov, Uri Zwick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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. The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is O(n 2), 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
Title of host publicationProceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
PublisherIEEE Computer Society
Pages663-672
Number of pages10
ISBN (Print)9780769542447
DOIs
StatePublished - 2010
Event2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, NV, United States
Duration: 23 Oct 201026 Oct 2010

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010
Country/TerritoryUnited States
CityLas Vegas, NV
Period23/10/1026/10/10

Keywords

  • Graph algorithms
  • Shortest paths

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