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All-Pairs Shortest Paths for Real-Weighted Undirected Graphs with Small Additive Error

Author Timothy M. Chan

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Timothy M. Chan
  • Department of Computer Science, University of Illinois at Urbana-Champaign, IL, USA

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Timothy M. Chan. All-Pairs Shortest Paths for Real-Weighted Undirected Graphs with Small Additive Error. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 27:1-27:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.27

Abstract

Given a graph with n vertices and real edge weights in [0,1], we investigate an approximate version of the standard all-pairs shortest paths (APSP) problem where distances are estimated with additive error at most ε. Yuster (2012) introduced this natural variant of approximate APSP, and presented an algorithm for directed graphs running in Õ(n^{(3+ω)/2}) ≤ O(n^{2.687}) time for an arbitrarily small constant ε > 0, where ω denotes the matrix multiplication exponent. We give a faster algorithm for undirected graphs running in Õ(n^{(3+ω²)/(ω+1)}) ≤ O(n^{2.559}) time for any constant ε > 0. If ω = 2, the time bound is Õ(n^{7/3}), matching a previous result for undirected graphs by Dor, Halperin, and Zwick (2000) which only guaranteed additive error at most 2.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Shortest paths
  • approximation
  • matrix multiplication

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