Popular matchings in the marriage and roommates problems

Authors:
Péter Biró;Robert W. Irving;David F. Manlove
Affiliations:
Department of Computing Science, University of Glasgow, Glasgow, UK;Department of Computing Science, University of Glasgow, Glasgow, UK;Department of Computing Science, University of Glasgow, Glasgow, UK
Venue:
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Year:
2010

Citing 17
Cited 5

The stable marriage problem: structure and algorithms

The stable marriage problem: structure and algorithms
NP-complete stable matching problems

Journal of Algorithms
Faster scaling algorithms for general graph matching problems

Journal of the ACM (JACM)
Scaling Algorithms for the Shortest Paths Problem

SIAM Journal on Computing
An Efficient Implementation of Edmonds' Algorithm for Maximum Matching on Graphs

Journal of the ACM (JACM)
Unique maximum matching algorithms

Journal of Algorithms
Hard variants of stable marriage

Theoretical Computer Science
Stable Marriage with Incomplete Lists and Ties

ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Random popular matchings

EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Popular matchings in the capacitated house allocation problem

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Popular Matchings

SIAM Journal on Computing
Bounded Unpopularity Matchings

SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Popular Matchings: Structure and Algorithms

COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Popular matchings in the weighted capacitated house allocation problem

Journal of Discrete Algorithms
The least-unpopularity-factor and least-unpopularity-margin criteria for matching problems with one-sided preferences

LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Dynamic matching markets and voting paths

SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Weighted popular matchings

ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I

Popular matchings in the stable marriage problem

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Near-popular matchings in the roommates problem

ESA'11 Proceedings of the 19th European conference on Algorithms
Popularity vs maximum cardinality in the stable marriage setting

Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Popular matchings in the stable marriage problem

Information and Computation
Computing desirable partitions in additively separable hedonic games

Artificial Intelligence

Quantified Score

Hi-index	0.00

Visualization

Abstract

Popular matchings have recently been a subject of study in the context of the so-called House Allocation Problem, where the objective is to match applicants to houses over which the applicants have preferences. A matching M is called popular if there is no other matching M′ with the property that more applicants prefer their allocation in M′ to their allocation in M. In this paper we study popular matchings in the context of the Roommates Problem, including its special (bipartite) case, the Marriage Problem. We investigate the relationship between popularity and stability, and describe efficient algorithms to test a matching for popularity in these settings. We also show that, when ties are permitted in the preferences, it is NP-hard to determine whether a popular matching exists in both the Roommates and Marriage cases.