## 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(n^{2}), 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(log^{2} n) expected time.

Original language | English |
---|---|

Title of host publication | Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |

Publisher | IEEE Computer Society |

Pages | 663-672 |

Number of pages | 10 |

ISBN (Print) | 9780769542447 |

DOIs | |

State | Published - 2010 |

Event | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 - Las Vegas, NV, United States Duration: 23 Oct 2010 → 26 Oct 2010 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
---|---|

ISSN (Print) | 0272-5428 |

### Conference

Conference | 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 |
---|---|

Country/Territory | United States |

City | Las Vegas, NV |

Period | 23/10/10 → 26/10/10 |

## Keywords

- Graph algorithms
- Shortest paths

## Fingerprint

Dive into the research topics of 'All-pairs shortest paths in O(n^{2}) time with high probability'. Together they form a unique fingerprint.