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Computer Science > Data Structures and Algorithms

arXiv:1802.07440 (cs)
[Submitted on 21 Feb 2018]

Title:Max-size popular matchings and extensions

Authors:Telikepalli Kavitha
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Abstract:We consider the max-size popular matching problem in a roommates instance G = (V,E) with strict preference lists. A matching M is popular if there is no matching M' in G such that the vertices that prefer M' to M outnumber those that prefer M to M'. We show it is NP-hard to compute a max-size popular matching in G. This is in contrast to the tractability of this problem in bipartite graphs where a max-size popular matching can be computed in linear time. We define a subclass of max-size popular matchings called strongly dominant matchings and show a linear time algorithm to solve the strongly dominant matching problem in a roommates instance.
We consider a generalization of the max-size popular matching problem in bipartite graphs: this is the max-weight popular matching problem where there is also an edge weight function w and we seek a popular matching of largest weight. We show this is an NP-hard problem and this is so even when w(e) is either 1 or 2 for every edge e. We also show an algorithm with running time O*(2^{n/4}) to find a max-weight popular matching matching in G = (A U B,E)$ on n vertices.
Comments: 26 pages, 10 figures
Subjects: Data Structures and Algorithms (cs.DS)
Cite as: arXiv:1802.07440 [cs.DS]
  (or arXiv:1802.07440v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.1802.07440

Submission history

From: Telikepalli Kavitha [view email]
[v1] Wed, 21 Feb 2018 06:43:21 UTC (55 KB)
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