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The classical Stable Roommates problem is to decide whether there exists amatching of an even number of agents such that no two agents which are notmatched to each other would prefer to be with each other rather than with theirrespectively assigned partners. We investigate Stable Roommates with complete(i.e., every agent can be matched with any other agent) or incompletepreferences, with ties (i.e., two agents are considered of equal value to someagent) or without ties. It is known that in general allowing ties makes theproblem NP-complete. We provide algorithms for Stable Roommates that are,compared to those in the literature, more efficient when the input preferencesare complete and have some structural property, such as being narcissistic,single-peaked, and single-crossing. However, when the preferences areincomplete and have ties, we show that being single-peaked and single-crossingdoes not reduce the computational complexity--Stable Roommates remainsNP-complete.

Stable Roommates with Narcissistic, Single-Peaked, and Single-Crossing Preferences