Optimal stable matchings in Stable Roommates instances are fixed-parameter tractable parameterized by the minimum crossing distance to Stable Marriage instances.
Complexity of the sex-equal stable marriage problem.Japan Journal of Industrial and Applied Mathematics, 10(1):1, February 1993
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Bridging the Gap Between Stable Marriage and Stable Roommates: A Parameterized Algorithm for Optimal Stable Matchings
Optimal stable matchings in Stable Roommates instances are fixed-parameter tractable parameterized by the minimum crossing distance to Stable Marriage instances.