### 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 | Distributed Computing - 25th International Symposium, DISC 2011, Proceedings |

Pages | 200-201 |

Number of pages | 2 |

DOIs | |

State | Published - Nov 2 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) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### 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 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Distributed Computing - 25th International Symposium, DISC 2011, Proceedings*(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