Fair Matchings and Related Problems
Artikel i vetenskaplig tidskrift, 2016

Let G = (A boolean OR B, E) be a bipartite graph, where every vertex ranks its neighbors in an order of preference (with ties allowed) and let r be the worst rank used. A matching M is fair in G if it has maximum cardinality, subject to this, M matches the minimum number of vertices to rank r neighbors, subject to that, M matches the minimum number of vertices to rank (r - 1) neighbors, and so on. We show an efficient combinatorial algorithm based on LP duality to compute a fair matching in G. We also show a scaling based algorithm for the fair b-matching problem. Our two algorithms can be extended to solve other profile-based matching problems. In designing our combinatorial algorithm, we show how to solve a generalized version of the minimum weighted vertex cover problem in bipartite graphs, using a single-source shortest paths computation-this can be of independent interest.

Bipartite graphs

Profile-based matching

Matching under preferences

Författare

Chien-Chung Huang

Chalmers, Data- och informationsteknik, Datavetenskap

T. Kavitha

Tata Institute of Fundamental Research

K. Mehlhorn

Max Planck-institutet

D. Michail

Harokopio Panepistimio

Algorithmica

0178-4617 (ISSN) 1432-0541 (eISSN)

Vol. 74 3 1184-1203

Ämneskategorier

Datavetenskap (datalogi)

DOI

10.1007/s00453-015-9994-9