Simplifying and unifying replacement paths algorithms in weighted directed graphs

Shiri Chechik, Moran Nechushtan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

In the replacement paths (RP) problem we are given a graph G and a shortest path P between two nodes s and t 1. The goal is to find for every edge e ∈ P, a shortest path from s to t that avoids e. The first result of this paper is a simple reduction from the RP problem to the problem of computing shortest cycles for all nodes on a shortest path. Using this simple reduction we unify and extremely simplify two state of the art solutions for two different well-studied variants of the RP problem. In the first variant (algebraic) we show that by using at most n queries to the Yuster-Zwick distance oracle [FOCS 2005], one can solve the the RP problem for a given directed graph with integer edge weights in the range [−M, M] in Õ (Mnω) time 2 3 . This improves the running time of the state of the art algorithm of Vassilevska Williams [SODA 2011] by a factor of log6 n. In the second variant (planar) we show that by using the algorithm of Klein for the multiple-source shortest paths problem (MSSP) [SODA 2005] one can solve the RP problem for directed planar graph with non negative edge weights in O (n log n) time. This matches the state of the art algorithm of Wulff-Nilsen [SODA 2010], but with arguably much simpler algorithm and analysis.

Original languageEnglish
Title of host publication47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
EditorsArtur Czumaj, Anuj Dawar, Emanuela Merelli
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771382
DOIs
StatePublished - 1 Jun 2020
Event47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 - Virtual, Online, Germany
Duration: 8 Jul 202011 Jul 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume168
ISSN (Print)1868-8969

Conference

Conference47th International Colloquium on Automata, Languages, and Programming, ICALP 2020
Country/TerritoryGermany
CityVirtual, Online
Period8/07/2011/07/20

Funding

FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Horizon 2020803118

    Keywords

    • Distance oracle
    • Fault tolerance
    • Planar graph

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