Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs

Andrzej Czygrinow; Michał Hańćkowiak; Edyta Szymańska

doi:10.1007/978-3-642-10631-6_68

Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs

Andrzej Czygrinow, Michał Hańćkowiak, Edyta Szymańska

Mathematical and Statistical Sciences, School of (SoMSS)

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

11 Scopus citations

Abstract

We give a deterministic distributed approximation algorithm for the maximum matching problem in graphs of bounded arboricity. Specifically, given 0<ε<1 and a positive integer a, the algorithm finds a matching of size at least (1-ε)m(G), where m(G) is the size of the maximum matching in an n-vertex graph G with arboricity at most a. The algorithm runs in O(log ^* n) rounds in the message passing model and it is the first sublogarithmic algorithm for the problem on such a wide class of graphs. Moreover, the result implies that the known lower bound on the time complexity for a constant or polylogarithmic approximation does not hold for graphs of bounded arboricity.

Original language	English (US)
Title of host publication	Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings
Pages	668-678
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-10631-6_68
State	Published - 2009
Event	20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States Duration: Dec 16 2009 → Dec 18 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5878 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	20th International Symposium on Algorithms and Computation, ISAAC 2009
Country/Territory	United States
City	Honolulu, HI
Period	12/16/09 → 12/18/09

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-10631-6_68

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Czygrinow, A., Hańćkowiak, M., & Szymańska, E. (2009). Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings (pp. 668-678). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS). https://doi.org/10.1007/978-3-642-10631-6_68

Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. / Czygrinow, Andrzej; Hańćkowiak, Michał; Szymańska, Edyta.
Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. p. 668-678 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5878 LNCS).

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

Czygrinow, A, Hańćkowiak, M & Szymańska, E 2009, Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. in Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5878 LNCS, pp. 668-678, 20th International Symposium on Algorithms and Computation, ISAAC 2009, Honolulu, HI, United States, 12/16/09. https://doi.org/10.1007/978-3-642-10631-6_68

Czygrinow A, Hańćkowiak M, Szymańska E. Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. In Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. p. 668-678. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-10631-6_68

Czygrinow, Andrzej ; Hańćkowiak, Michał ; Szymańska, Edyta. / Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. Algorithms and Computation - 20th International Symposium, ISAAC 2009, Proceedings. 2009. pp. 668-678 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs

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