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research
The Maximum-Weight Stable Matching Problem: Duality and Efficiency
Authors
X Chen
G Ding
X Hu
W Zang
Publication date
1 January 2012
Publisher
'Society for Industrial & Applied Mathematics (SIAM)'
Doi
Cite
Abstract
Given a preference system (G,≺) and an integral weight function defined on the edge set of G (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of (G,≺) with maximum total weight. In this paper we study this NP-hard problem using linear programming and polyhedral approaches. We show that the Rothblum system for defining the fractional stable matching polytope of (G,≺) is totally dual integral if and only if this polytope is integral if and only if (G,≺) has a bipartite representation. We also present a combinatorial polynomial-time algorithm for the maximum-weight stable matching problem and its dual on any preference system with a bipartite representation. Our results generalize Király and Pap's theorem on the maximum-weight stable-marriage problem and rely heavily on their work. © 2012 Society for Industrial and Applied Mathematics.published_or_final_versio
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info:doi/10.1137%2F120864866
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