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

Nikhil Bansal; Niv Buchbinder; Anupam Gupta; Joseph Naor

doi:10.1007/978-3-540-75520-3_47

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

Nikhil Bansal^*, Niv Buchbinder, Anupam Gupta, Joseph Naor

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

27 Scopus citations

Abstract

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 language	English
Title of host publication	Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
Publisher	Springer Verlag
Pages	522-533
Number of pages	12
ISBN (Print)	9783540755197
DOIs	https://doi.org/10.1007/978-3-540-75520-3_47
State	Published - 2007
Externally published	Yes
Event	15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel Duration: 8 Oct 2007 → 10 Oct 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4698 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	15th Annual European Symposium on Algorithms, ESA 2007
Country/Territory	Israel
City	Eilat
Period	8/10/07 → 10/10/07

Access to Document

10.1007/978-3-540-75520-3_47

Cite this

Bansal, N., Buchbinder, N., Gupta, A., & Naor, J. (2007). An O(log² k)-competitive algorithm for metric bipartite matching. In Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings (pp. 522-533). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4698 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-75520-3_47

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Bansal, N, Buchbinder, N, Gupta, A & Naor, J 2007, An O(log² k)-competitive algorithm for metric bipartite matching. in Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4698 LNCS, Springer Verlag, pp. 522-533, 15th Annual European Symposium on Algorithms, ESA 2007, Eilat, Israel, 8/10/07. https://doi.org/10.1007/978-3-540-75520-3_47

An O(log² k)-competitive algorithm for metric bipartite matching. / Bansal, Nikhil; Buchbinder, Niv; Gupta, Anupam et al.
Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Springer Verlag, 2007. p. 522-533 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4698 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bansal N, Buchbinder N, Gupta A, Naor J. An O(log² k)-competitive algorithm for metric bipartite matching. In Algorithms - ESA 2007 - 15th Annual European Symposium, Proceedings. Springer Verlag. 2007. p. 522-533. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-75520-3_47