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Cseh, Ágnes
Kavitha, Telikepalli
Year of Publication: 
Series/Report no.: 
CERS-IE Working Papers No. CERS-IE WP - 2020/4
Our input is a complete graph G on n vertices where each vertex has a strictranking of all other vertices in G. The goal is to construct a matching in G that is "globallystable" or popular. A matching M is popular if M does not lose a head-to-head election againstany matching M': here each vertex casts a vote forthe matching in {M,M'} in which it gets abetter assignment. Popular matchings need not exist in the given instance G and the popularmatching problem is to decide whether one exists or not. The popular matching problem in Gis easy to solve for odd n. Surprisingly, the problem becomes NP-hard for even n, as we showhere. This seems to be the first graph theoretic problem that is efficiently solvable when n hasone parity and NP-hard when n has the other parity.
popular matching
polynomial algorithm
stable matching
Document Type: 
Working Paper

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