All-pairs shortest paths with a sublinear additive error

Liam Roditty, Asaf Shapira

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

4 Scopus citations

Abstract

We show that for every 0 ≤ p ≤ 1 there is an algorithm with running time of O(n2.575-p/(7.4-2.3p)) that given a directed graph with small positive integer weights, estimates the length of the shortest path between every pair of vertices u,v in the graph to within an additive error δp (u,v), where δ(u,v) is the exact length of the shortest path between u and v. This algorithm runs faster than the fastest algorithm for computing exact shortest paths for any 0 < p ≤ 1. Previously the only way to "bit" the running time of the exact shortest path algorithms was by applying an algorithm of Zwick [FOCS '98] that approximates the shortest path distances within a multiplicative error of (1 + ε). Our algorithm thus gives a smooth qualitative and quantitative transition between the fastest exact shortest paths algorithm, and the fastest approximation algorithm with a linear additive error. In fact, the main ingredient we need in order to obtain the above result, which is also interesting in its own right, is an algorithm for computing (1 + ε) multiplicative approximations for the shortest paths, whose running time is faster than the running time of Zwick's approximation algorithm when ε ≪ 1 and the graph has small integer weights.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 35th International Colloquium, ICALP 2008, Proceedings
Pages622-633
Number of pages12
EditionPART 1
DOIs
StatePublished - 2008
Externally publishedYes
Event35th International Colloquium on Automata, Languages and Programming, ICALP 2008 - Reykjavik, Iceland
Duration: 7 Jul 200811 Jul 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5125 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference35th International Colloquium on Automata, Languages and Programming, ICALP 2008
Country/TerritoryIceland
CityReykjavik
Period7/07/0811/07/08

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