Popular Matchings in Complete Graphs
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.
popular matching
complete graph
complexity
linear programming
Theory of computation~Graph algorithms analysis
17:1-17:14
Regular Paper
https://arxiv.org/pdf/1807.01112.pdf
Ágnes
Cseh
Ágnes Cseh
Hungarian Academy of Sciences, Budapest, Hungary
Supported by the Cooperation of Excellences Grant (KEP-6/2017), by the Ministry of Human Resources under its New National Excellence Programme (ÚNKP-18-4-BME-331), the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2016), its János Bolyai Research Fellowship, and OTKA grant K128611.
Telikepalli
Kavitha
Telikepalli Kavitha
Tata Institute of Fundamental Research, Mumbai, India
This work was done while visiting the Hungarian Academy of Sciences, Budapest.
10.4230/LIPIcs.FSTTCS.2018.17
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Ágnes Cseh and Telikepalli Kavitha
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