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

Andrzej Czygrinow, Michał Hańćkowiak, Edyta Szymańska

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

7 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages668-678
Number of pages11
Volume5878 LNCS
DOIs
StatePublished - 2009
Event20th International Symposium on Algorithms and Computation, ISAAC 2009 - Honolulu, HI, United States
Duration: Dec 16 2009Dec 18 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5878 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other20th International Symposium on Algorithms and Computation, ISAAC 2009
CountryUnited States
CityHonolulu, HI
Period12/16/0912/18/09

Fingerprint

Arboricity
Maximum Matching
Approximation algorithms
Matching Problem
Distributed Algorithms
Parallel algorithms
Approximation Algorithms
Graph in graph theory
Message passing
Message Passing
Time Complexity
Lower bound
Imply
Integer
Approximation
Vertex of a graph

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Czygrinow, A., Hańćkowiak, M., & Szymańska, E. (2009). Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5878 LNCS, 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5878 LNCS 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 proceedingConference contribution

Czygrinow, A, Hańćkowiak, M & Szymańska, E 2009, Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 5878 LNCS, 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 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5878 LNCS. 2009. p. 668-678. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 5878 LNCS 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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