eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-05
17:1
17:14
10.4230/LIPIcs.FSTTCS.2018.17
article
Popular Matchings in Complete Graphs
Cseh, Ágnes
1
Kavitha, Telikepalli
2
Hungarian Academy of Sciences, Budapest, Hungary
Tata Institute of Fundamental Research, Mumbai, India
Our input is a complete graph G = (V,E) on n vertices where each vertex has a strict ranking of all other vertices in G. The goal is to construct a matching in G that is "globally stable" or popular. A matching M is popular if M does not lose a head-to-head election against any matching M': here each vertex casts a vote for the matching in {M,M'} where it gets a better assignment. Popular matchings need not exist in the given instance G and the popular matching problem is to decide whether one exists or not. The popular matching problem in G is easy to solve for odd n. Surprisingly, the problem becomes NP-hard for even n, as we show here.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol122-fsttcs2018/LIPIcs.FSTTCS.2018.17/LIPIcs.FSTTCS.2018.17.pdf
popular matching
complete graph
complexity
linear programming