### Abstract

In this paper we consider the problem of matching clients with servers, each of which can process a subset of clients. It is known as the semi-matching or load balancing problem in a bipartite graph G = (V,U,E), where U corresponds to the clients, V to the 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 (d _{M} (v)+1/2) where d _{M} (v) is the degree of v 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. An optimal solution can be found sequentially in polynomial time but the distributed complexity is not well understood. Our algorithm yields (1 + 1/α)-approximation (where α = max{1, 1/2 (|U|/|V| + 1)}) and has time complexity O(Δ ^{5}), where Δ is the maximum degree of a vertex in V. In particular, for Δ = O(1) it gives constant approximation with constant time complexity. We also give a fast algorithm for the case when Δ is large and the degrees in V and U satisfy some additional properties. Both algorithms are deterministic.

Original language | English (US) |
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Title of host publication | Distributed Computing - 26th International Symposium, DISC 2012, Proceedings |

Pages | 210-222 |

Number of pages | 13 |

DOIs | |

State | Published - Nov 9 2012 |

Event | 26th International Symposium on Distributed Computing, DISC 2012 - Salvador, Brazil Duration: Oct 16 2012 → Oct 18 2012 |

### 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 | 7611 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 26th International Symposium on Distributed Computing, DISC 2012 |
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Country | Brazil |

City | Salvador |

Period | 10/16/12 → 10/18/12 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Distributed Computing - 26th International Symposium, DISC 2012, Proceedings*(pp. 210-222). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7611 LNCS). https://doi.org/10.1007/978-3-642-33651-5_15