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
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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
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
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The input is a bipartite graph G = (A ∪ B, E) where each vertex u ∈ A ∪ B ranks its neighbors in a strict order of preference. A matching M* is said to be popular if there is no matching M such that more vertices are better off in M than in M*. We consider the problem of computing a maximum cardinality popular matching in G. It is known that popular matchings always exist in such an instance G, however the complexity of computing a maximum cardinality popular matching was not known so far. In this paper we give a simple characterization of popular matchings when preference lists are strict and a sufficient condition for a maximum cardinality popular matching. We then show an O(mn0) algorithm for computing a maximum cardinality popular matching in G, where m = |E| and n0 = min(|A|, |B|).