Improved bounds for online preemptive matching

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

Abstract

When designing a preemptive online algorithm for the maximum matching problem, we wish to maintain a valid matching M while edges of the underlying graph are presented one after the other. When presented with an edge e, the algorithm should decide whether to augment the matching M by adding e (in which case e may be removed later on) or to keep M in its current form without adding e (in which case e is lost for good). The objective is to eventually hold a matching M with maximum weight. The main contribution of this paper is to establish new lower and upper bounds on the competitive ratio achievable by preemptive online algorithms: We provide a lower bound of 1 + ln 2 ≈ 1.693 on the competitive ratio of any randomized algorithm for the maximum cardinality matching problem, thus improving on the currently best known bound of e/(e - 1) ≈ 1.581 due to Karp, Vazirani, and Vazirani [STOC'90]. We devise a randomized algorithm that achieves an expected competitive ratio of 5.356 for maximum weight matching. This finding demonstrates the power of randomization in this context, showing how to beat the tight bound of 3+2p2 ≈ 5.828 for deterministic algorithms, obtained by combining the 5.828 upper bound of McGregor [APPROX'05] and the recent 5.828 lower bound of Varadaraja [ICALP'11].

Original languageEnglish
Title of host publication30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013
Pages389-399
Number of pages11
DOIs
StatePublished - 2013
Event30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013 - Kiel, Germany
Duration: 27 Feb 20132 Mar 2013

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume20
ISSN (Print)1868-8969

Conference

Conference30th International Symposium on Theoretical Aspects of Computer Science, STACS 2013
Country/TerritoryGermany
CityKiel
Period27/02/132/03/13

Keywords

  • Lower bound
  • Matching
  • Online algorithms

ASJC Scopus subject areas

  • Software

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