Online algorithms for maximum cardinality matching with edge arrivals

Niv Buchbinder, Danny Segev, Yevgeny Tkach

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

Abstract

In the adversarial edge arrival model for maximum cardinality matching, edges of an unknown graph are revealed one-by-one in arbitrary order, and should be irrevocably accepted or rejected. Here, the goal of an online algorithm is to maximize the number of accepted edges while maintaining a feasible matching at any point in time. For this model, the standard greedy heuristic is 1/2-competitive, and on the other hand, no algorithm that outperforms this ratio is currently known, even for very simple graphs. We present a clean Min-Index framework for devising a family of randomized algorithms, and provide a number of positive and negative results in this context. Among these results, we present a 5/9-competitive algorithm when the underlying graph is a forest, and prove that this ratio is best possible within the Min-Index framework. In addition, we prove a new general upper bound of 2 3+1/φ2≈0.5914 on the competitiveness of any algorithm in the edge arrival model. Interestingly, this bound holds even for an easier model in which vertices (along with their adjacent edges) arrive online, and when the underlying graph is a tree of maximum degree at most 3.

Original languageEnglish
Title of host publication25th European Symposium on Algorithms, ESA 2017
EditorsChristian Sohler, Christian Sohler, Kirk Pruhs
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770491
DOIs
StatePublished - 1 Sep 2017
Event25th European Symposium on Algorithms, ESA 2017 - Vienna, Austria
Duration: 4 Sep 20176 Sep 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume87
ISSN (Print)1868-8969

Conference

Conference25th European Symposium on Algorithms, ESA 2017
Country/TerritoryAustria
CityVienna
Period4/09/176/09/17

Bibliographical note

Publisher Copyright:
© Niv Buchbinder, Danny Segev, and Yevgeny Tkach.

Keywords

  • Competitive analysis
  • Maximum matching
  • Online algorithms
  • Primal-dual method

ASJC Scopus subject areas

  • Software

Cite this