The stable marriage problem: structure and algorithms
The stable marriage problem: structure and algorithms
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
SIAM Journal on Computing
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Note: Optimal popular matchings
Discrete Applied Mathematics
Popular Matchings: Structure and Algorithms
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Size versus stability in the marriage problem
Theoretical Computer Science
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Popularity vs maximum cardinality in the stable marriage setting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Popular matchings in the marriage and roommates problems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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We consider the problem of computing a maximum cardinality popular matching in a bipartite graph G=(A@?B,E) where each vertex u@?A@?B ranks its neighbors in a strict order of preference. Such a graph is called an instance of the stable marriage problem with strict preferences and incomplete lists. A matching M^@? is popular if for every matching M in G, the number of vertices that prefer M to M^@? is at most the number of vertices that prefer M^@? to M. Every stable matching of G is popular, however a stable matching is a minimum cardinality popular matching. The complexity of computing a maximum cardinality popular matching was unknown. In this paper we show a simple characterization of popular matchings in G=(A@?B,E). We also show a sufficient condition for a popular matching to be a maximum cardinality popular matching. We construct a matching that satisfies our characterization and sufficient condition in O(mn"0) time, where m=|E| and n"0=min(|A|,|B|). Thus the maximum cardinality popular matching problem in G=(A@?B,E) can be solved in O(mn"0) time.