### Abstract

We consider the semi-matching problem in bipartite graphs. The network is represented by a bipartite graph G = (U ∪ V, E), where U corresponds to clients, V to servers, and E is the set of available connections between them. The goal is to find a set of edges M ⊆ E such that every vertex in U is incident to exactly one edge in M. The load of a server v ε V is defined as the square of its degree in M and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. Formally, given a bipartite graph G = ∪ V,E), a semi-matching in G is a subgraph M such that deg _{M} (u) = 1 for every u ε U. A semi-matching M is called optimal if cost(M): = Σ _{v ε V} (deg _{M} (v))^{2} is minimal. It is not difficult to see that for any semi-matching M, where Δ is such that max _{v ε V} d(v) ≤ Δ. Consequently, if M* is optimal and M is arbitrary, then cost (M) ≤ Δ|V|cost(M*)/|U|. Our main result shows that in some networks the Δ|V|/|U| factor can be reduced to a constant (Theorem 1).

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 | 200-201 |

Number of pages | 2 |

Volume | 6950 LNCS |

DOIs | |

State | Published - 2011 |

Event | 25th International Symposium on Distributed Computing, DISC 2011 - Rome, Italy Duration: Sep 20 2011 → Sep 22 2011 |

### 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 | 6950 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 25th International Symposium on Distributed Computing, DISC 2011 |
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Country | Italy |

City | Rome |

Period | 9/20/11 → 9/22/11 |

### 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. 6950 LNCS, pp. 200-201). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6950 LNCS). https://doi.org/10.1007/978-3-642-24100-0_18

**Brief announcement : Distributed approximations for the semi-matching problem.** / Czygrinow, Andrzej; Hanćkowiak, Michal; Krzywdziński, Krzysztof; Szymańska, Edyta; Wawrzyniak, Wojciech.

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. 6950 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6950 LNCS, pp. 200-201, 25th International Symposium on Distributed Computing, DISC 2011, Rome, Italy, 9/20/11. https://doi.org/10.1007/978-3-642-24100-0_18

}

TY - GEN

T1 - Brief announcement

T2 - Distributed approximations for the semi-matching problem

AU - Czygrinow, Andrzej

AU - Hanćkowiak, Michal

AU - Krzywdziński, Krzysztof

AU - Szymańska, Edyta

AU - Wawrzyniak, Wojciech

PY - 2011

Y1 - 2011

N2 - We consider the semi-matching problem in bipartite graphs. The network is represented by a bipartite graph G = (U ∪ V, E), where U corresponds to clients, V to servers, and E is the set of available connections between them. The goal is to find a set of edges M ⊆ E such that every vertex in U is incident to exactly one edge in M. The load of a server v ε V is defined as the square of its degree in M and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. Formally, given a bipartite graph G = ∪ V,E), a semi-matching in G is a subgraph M such that deg M (u) = 1 for every u ε U. A semi-matching M is called optimal if cost(M): = Σ v ε V (deg M (v))2 is minimal. It is not difficult to see that for any semi-matching M, where Δ is such that max v ε V d(v) ≤ Δ. Consequently, if M* is optimal and M is arbitrary, then cost (M) ≤ Δ|V|cost(M*)/|U|. Our main result shows that in some networks the Δ|V|/|U| factor can be reduced to a constant (Theorem 1).

AB - We consider the semi-matching problem in bipartite graphs. The network is represented by a bipartite graph G = (U ∪ V, E), where U corresponds to clients, V to servers, and E is the set of available connections between them. The goal is to find a set of edges M ⊆ E such that every vertex in U is incident to exactly one edge in M. The load of a server v ε V is defined as the square of its degree in M and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. Formally, given a bipartite graph G = ∪ V,E), a semi-matching in G is a subgraph M such that deg M (u) = 1 for every u ε U. A semi-matching M is called optimal if cost(M): = Σ v ε V (deg M (v))2 is minimal. It is not difficult to see that for any semi-matching M, where Δ is such that max v ε V d(v) ≤ Δ. Consequently, if M* is optimal and M is arbitrary, then cost (M) ≤ Δ|V|cost(M*)/|U|. Our main result shows that in some networks the Δ|V|/|U| factor can be reduced to a constant (Theorem 1).

UR - http://www.scopus.com/inward/record.url?scp=80055057821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80055057821&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24100-0_18

DO - 10.1007/978-3-642-24100-0_18

M3 - Conference contribution

AN - SCOPUS:80055057821

SN - 9783642240997

VL - 6950 LNCS

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

SP - 200

EP - 201

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

ER -