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Popular Matchings in Complete Graphs

Agnes Cseh () and Telikepalli Kavitha ()
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Agnes Cseh: Centre for Economic and Regional Studies, Institute of Economics
Telikepalli Kavitha: Tata Institute of Fundamental Research, Mumbai, India

No 2004, CERS-IE WORKING PAPERS from Institute of Economics, Centre for Economic and Regional Studies

Abstract: 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.

Keywords: popularmatching; NP-completeness; polynomial algorithm; stable matching (search for similar items in EconPapers)
JEL-codes: C63 C78 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2020-04
New Economics Papers: this item is included in nep-des
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