## Abstract

The Stable Matching problem was introduced by Gale and Shapley in 1962. The input for the stable matching problem is a complete bipartite K_{n,n} graph together with a ranking for each node. Its output is a matching that does not contain a blocking pair, where a blocking pair is a pair of elements that are not matched together but rank each other higher than they rank their current mates. In this work we study the Distributed Weighted Stable Matching problem. The input to the Weighted Stable Matching problem is a complete bipartite K _{n,n} graph and a weight function W. The ranking of each node is determined by W, i.e. node v prefers node u_{1} over node u_{2} if W((v,u_{1})) > W((v, u_{2})). Using this ranking we can solve the original Stable Matching problem. We consider two different communication models: the billboard model and the full distributed model. In the billboard model, we assume that there is a public billboard and each participant can write one message on it in each time step. In the distributed model, we assume that each node can send O(log n) bits on each edge of the K_{n,n}. In the billboard model we prove a somewhat surprising tight bound: any algorithm that solves the Stable Matching problem requires at least n - 1 rounds. We provide an algorithm that meets this bound. In the distributed communication model we provide an algorithm named intermediation agencies algorithm, in short (IAA), that solves the Distributed Weighted Stable Marriage problem in O(√n) rounds. This is the first sub-linear distributed algorithm that solves some subcase of the general Stable Marriage problem.

Original language | English |
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Title of host publication | Structural Information and Communication Complexity - 17th International Colloquium, SIROCCO 2010, Proceedings |

Pages | 29-40 |

Number of pages | 12 |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | 17th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2010 - Sirince, Turkey Duration: 7 Jun 2010 → 11 Jun 2010 |

### 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 | 6058 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 17th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2010 |
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Country/Territory | Turkey |

City | Sirince |

Period | 7/06/10 → 11/06/10 |

## Keywords

- Billboard
- Distributed Algorithms
- Matching
- Scheduling
- Stable Marriage