### 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) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 668-678 |

Number of pages | 11 |

Volume | 5878 LNCS |

DOIs | |

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) |
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Volume | 5878 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 20th International Symposium on Algorithms and Computation, ISAAC 2009 |
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Country | United States |

City | Honolulu, HI |

Period | 12/16/09 → 12/18/09 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

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

*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

}

TY - GEN

T1 - Fast distributed approximation algorithm for the maximum matching problem in bounded arboricity graphs

AU - Czygrinow, Andrzej

AU - Hańćkowiak, Michał

AU - Szymańska, Edyta

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=75649085309&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75649085309&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-10631-6_68

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

M3 - Conference contribution

AN - SCOPUS:75649085309

SN - 3642106307

SN - 9783642106309

VL - 5878 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 668

EP - 678

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -