### Abstract

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 and V to the servers. 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∈V is defined as (deg_{M}(v)+12), and the problem is to find a semi-matching M that minimizes the sum of the loads of the servers. We show that to find an optimal solution in a distributed setting Ω(|V|) rounds are needed and propose distributed deterministic approximation algorithms for the problem. It yields 2-approximation and has time complexity O(Δ^{5}), where Δ is the maximum degree in V. We also give some greedy algorithms.

Original language | English (US) |
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Pages (from-to) | 1251-1267 |

Number of pages | 17 |

Journal | Journal of Computer and System Sciences |

Volume | 82 |

Issue number | 8 |

DOIs | |

State | Published - Dec 1 2016 |

### Keywords

- Distributed algorithms
- Semi-matching

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*Journal of Computer and System Sciences*,

*82*(8), 1251-1267. https://doi.org/10.1016/j.jcss.2016.05.001