Near optimal algorithm for the directed single source replacement paths problem

Shiri Chechik, Ofer Magen

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

7 Scopus citations

Abstract

In the Single Source Replacement Paths (SSRP) problem we are given a graph G = (V, E), and a shortest paths tree Kb rooted at a node s, and the goal is to output for every node t ∈ V and for every edge e in Kb the length of the shortest path from s to t avoiding e. We present an Õ(m√n + n2) time randomized combinatorial algorithm for unweighted directed graphs1. Previously such a bound was known in the directed case only for the seemingly easier problem of replacement path where both the source and the target nodes are fixed. Our new upper bound for this problem matches the existing conditional combinatorial lower bounds. Hence, (assuming these conditional lower bounds) our result is essentially optimal and completes the picture of the SSRP problem in the combinatorial setting. Our algorithm naturally extends to the case of small, rational edge weights. In the full version of the paper, we strengthen the existing conditional lower bounds in this case by showing that any O(mn1/2−ε) time (combinatorial or algebraic) algorithm for some fixed ε > 0 yields a truly sub-cubic algorithm for the weighted All Pairs Shortest Paths problem (previously such a bound was known only for the combinatorial setting).

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 Programme803118
European Research Council

    Keywords

    • Combinatorial algorithms
    • Conditional lower bounds
    • Fault tolerance
    • Replacement Paths

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