The cycle roommates problem: a hard case of kidney exchange

Recently, a number of interesting algorithmic problems have arisen from the emergence, in a number of countries, of kidney exchange schemes, whereby live donors are matched with recipients according to compatibility and other considerations. One such problem can be modeled by a variant of the well-known stable roommates problem in which blocking cycles, as well as the normal blocking pairs, are significant. We show here that this variant of the stable roommates problem is NP-complete, thus solving an open question posed by Cechl´arov´a and Lacko. 1 Background and problem statement An instance of the stable roommates problem (SR) consists of a set of participants {p1, . . . , pn}, and for each participant, a preference list, which is a total order over a subset of the others. We say that pj is acceptable to pi if pj appears on pi’s preference list, and that pi prefers pj to pk if pj and pk are both acceptable to pi and pj precedes pk on pi’s list. An acceptable pair is a pair {p...

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Robert W. Irving
• Keywords: Interesting Algorithmic Problems, IPL 2007, Stable Roommates Problem, Well-known Stable Roommates