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Title: The geometry of fractional stable matchings and its applications
Authors: Teo, C.-P. 
Sethuraman, J.
Keywords: Approximation algorithms
Linear programming
Stable matching
Issue Date: 1998
Citation: Teo, C.-P.,Sethuraman, J. (1998). The geometry of fractional stable matchings and its applications. Mathematics of Operations Research 23 (4) : 874-891. ScholarBank@NUS Repository.
Abstract: We study the classical stable marriage and stable roommates problems using a polyhedral approach. We propose a new LP formulation for the stable roommates problem, which has a feasible solution if and only if the underlying roommates problem has a stable matching. Furthermore, for certain special weight functions on the edges, we construct a 2-approximation algorithm for the optimal stable roommates problem. Our technique exploits features of the geometry of fractional solutions of this formulation. For the stable marriage problem, we show that a related geometry allows us to express any fractional solution in the stable marriage polytope as a convex combination of stable marriage solutions. This also leads to a genuinely simple proof of the integrality of the stable marriage polytope.
Source Title: Mathematics of Operations Research
ISSN: 0364765X
Appears in Collections:Staff Publications

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