An O(log2 k)-competitive algorithm for metric bipartite matching

Nikhil Bansal, Niv Buchbinder, Anupam Gupta, Joseph Naor

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider the online metric matching problem. In this problem, we are given a graph with edge weights satisfying the triangle inequality, and k vertices that are designated as the right side of the matching. Over time up to k requests arrive at an arbitrary subset of vertices in the graph and each vertex must be matched to a right side vertex immediately upon arrival. A vertex cannot be rematched to another vertex once it is matched. The goal is to minimize the total weight of the matching. We give a O(log2 k) competitive randomized algorithm for the problem. This improves upon the best known guarantee of O(log3 k) due to Meyerson, Nanavati and Poplawski [19]. It is well known that no deterministic algorithm can have a competitive less than 2k - 1, and that no randomized algorithm can have a competitive ratio of less than In k.

Original languageEnglish (US)
Title of host publicationAlgorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540755197
StatePublished - 2007
Event15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel
Duration: Oct 8 2007Oct 10 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4698 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th Annual European Symposium on Algorithms, ESA 2007

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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