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DOI: 10.4230/LIPIcs.FSTTCS.2018.17
URN: urn:nbn:de:0030-drops-99164
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9916/
Cseh, Ágnes ; Kavitha, Telikepalli
Popular Matchings in Complete Graphs
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Abstract
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.
BibTeX - Entry
@InProceedings{cseh_et_al:LIPIcs:2018:9916,
author = {Ágnes Cseh and Telikepalli Kavitha},
title = {{Popular Matchings in Complete Graphs}},
booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
pages = {17:1--17:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-093-4},
ISSN = {1868-8969},
year = {2018},
volume = {122},
editor = {Sumit Ganguly and Paritosh Pandya},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9916},
URN = {urn:nbn:de:0030-drops-99164},
doi = {10.4230/LIPIcs.FSTTCS.2018.17},
annote = {Keywords: popular matching, complete graph, complexity, linear programming}
}
| Keywords: | popular matching, complete graph, complexity, linear programming | |
| Seminar: | 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 05.12.2018 |
