## 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 language | English |
---|---|

Article number | 26 |

Journal | Journal of the ACM |

Volume | 60 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2013 |

## Keywords

- Probabilistic analysis
- Shortest paths