Note: Optimal popular matchings

Authors:
Telikepalli Kavitha;Meghana Nasre
Affiliations:
Indian Institute of Science, Bangalore, India;Indian Institute of Science, Bangalore, India
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 5
Cited 3

An efficient algorithm for the “optimal” stable marriage

Journal of the ACM (JACM)
The stable marriage problem: structure and algorithms

The stable marriage problem: structure and algorithms
Random popular matchings

EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Rank-maximal matchings

ACM Transactions on Algorithms (TALG)
Popular Matchings

SIAM Journal on Computing

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
Popularity at minimum cost

Journal of Combinatorial Optimization

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Abstract

In this paper we consider the problem of computing an ''optimal'' popular matching. We assume that our input instance G=(A@?P,E"1@?@?...@?@?E"r) admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness in which case we are required to return a fair popular matching. We show an O(n^2+m) algorithm for this problem, assuming that the preference lists are strict, where m is the number of edges in G and n is the number of applicants.