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Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.22
URN: urn:nbn:de:0030-drops-63011
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6301/
Kavitha, Telikepalli
Popular Half-Integral Matchings
Abstract
In an instance G = (A union B, E) of the stable marriage problem with strict and possibly incomplete preference lists, a matching M is popular if there is no matching M0 where the vertices that prefer M' to M outnumber those that prefer M to M'. All stable matchings are popular and there is a simple linear time algorithm to compute a maximum-size popular matching. More generally, what we seek is a min-cost popular matching where we assume there is a cost function c : E -> Q. However there is no polynomial time algorithm currently known for solving this problem. Here we consider the following generalization of a popular matching called a popular half-integral matching: this is a fractional matching ~x = (M_1 + M_2)/2, where M1 and M2 are the 0-1 edge incidence vectors of matchings in G, such that ~x satisfies popularity constraints. We show that every popular half-integral matching is equivalent to a stable matching in a larger graph G^*. This allows us to solve the min-cost popular half-integral matching problem in polynomial time.
BibTeX - Entry
@InProceedings{kavitha:LIPIcs:2016:6301,
author = {Telikepalli Kavitha},
title = {{Popular Half-Integral Matchings}},
booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
pages = {22:1--22:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-013-2},
ISSN = {1868-8969},
year = {2016},
volume = {55},
editor = {Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6301},
URN = {urn:nbn:de:0030-drops-63011},
doi = {10.4230/LIPIcs.ICALP.2016.22},
annote = {Keywords: bipartite graphs, stable matchings, fractional matchings, polytopes}
}
Keywords: |
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bipartite graphs, stable matchings, fractional matchings, polytopes |
Collection: |
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43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) |
Issue Date: |
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2016 |
Date of publication: |
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23.08.2016 |