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The Cartographer
The Popular Roommates problem
March 31, 2018 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Telikepalli Kavitha
arXiv ID
1804.00141
Category
cs.DS: Data Structures & Algorithms
Citations
2
Venue
arXiv.org
Last Checked
4 months ago
Abstract
We consider the popular matching problem in a roommates instance with strict preference lists. While popular matchings always exist in a bipartite instance, they need not exist in a roommates instance. The complexity of the popular matching problem in a roommates instance has been an open problem for several years and here we show it is NP-hard. A sub-class of max-size popular matchings called dominant matchings has been well-studied in bipartite graphs. We show that the dominant matching problem in a roommates instance is also NP-hard and this is the case even when the instance admits a stable matching.
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