Random Stable Roommates instances are typically nearly solvable: they have few odd cycles that block stability, and the stable matchings or partitions they admit are usually few, which makes many NP-hard optimization problems easy in practice.
Small random instances of the stable roommates problem
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Perspectives on Unsolvability in the Roommates Problem
Random Stable Roommates instances are typically nearly solvable: they have few odd cycles that block stability, and the stable matchings or partitions they admit are usually few, which makes many NP-hard optimization problems easy in practice.