Optimal stable matchings in Stable Roommates instances are fixed-parameter tractable parameterized by the minimum crossing distance to Stable Marriage instances.
The Structure of the Stable Roommate Problem: Efficient Representation and Enumeration of All Stable Assignments.SIAM Journal on Computing, 17(4):742–769, August 1988
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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.