Replacement paths and k simple shortest paths in unweighted directed graphs

Liam Roditty*, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

51 Scopus citations

Abstract

Let G = (V, E) be a directed graph and let P be a shortest path from s to t in G. In the replacement paths problem we are required to find, for every edge e on P, a shortest path from s to t in G that avoids e. We present the first non-trivial algorithm for computing replacement paths in unweighted directed graphs (and in graphs with small integer weights). Our algorithm is Monte-Carlo and its running time is Õ(m√n). Using the improved algorithm for the replacement paths problem we get an improved algorithm for finding the k simple shortest paths between two given vertices.

Original languageEnglish
Pages (from-to)249-260
Number of pages12
JournalLecture Notes in Computer Science
Volume3580
DOIs
StatePublished - 2005
Event32nd International Colloquium on Automata, Languages and Programming, ICALP 2005 - Lisbon, Portugal
Duration: 11 Jul 200515 Jul 2005

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