Optimal stable matchings in Stable Roommates instances are fixed-parameter tractable parameterized by the minimum crossing distance to Stable Marriage instances.
On Treewidth and Stable Marriage: Parameterized Algorithms and Hardness Results (Complete Characterization).SIAM Journal on Discrete Mathematics, 36(1):596–681, March 2022
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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.