## Abstract

Two vertices in a weighted directed graph may be connected by many shortest paths. Although all these paths are shortest in terms of weight, the number of edges on them may vary substantially, which leads in considering the all pairs lightest shortest paths (APLSP) problem. A solution to this problem is a representation of shortest paths between all of pairs of vertices in the graph such that each of these shortest paths uses a minimal, or a close to minimal, number of edges. Algorithms for obtaining exact or approximate solutions to the APLSP problem are presented. These results extend the results obtained recently for the all pairs shortest paths (APSP) problem.

Original language | English |
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Pages (from-to) | 61-69 |

Number of pages | 9 |

Journal | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - 1999 |

Event | Proceedings of the 1999 31st Annual ACM Symposium on Theory of Computing - FCRC '99 - Atlanta, GA, USA Duration: 1 May 1999 → 4 May 1999 |