Three-Sided Stable Matchings with Cyclic Preferences

Knuth [14] asked whether the stable matching problem can be generalised to three dimensions i. e., for families containing a man, a woman and a dog. Subsequently, several authors considered the three-sided stable matching problem with cyclic preferences, where men care only about women, women only about dogs, and dogs only about men. In this paper we prove that if the preference lists may be incomplete, then the problem of deciding whether a stable matching exists, given an instance of three-sided stable matching problem with cyclic preferences is NP-complete. Considering an alternative stability criterion, strong stability, we show that the problem is NP-complete even for complete lists. These problems can be regarded as special types of stable exchange problems, therefore these results have relevance in some real applications, such as kidney exchange programs.

• Type: Journal
• Year: 2010
• Where: ALGORITHMICA
• Authors: Péter Biró, Eric McDermid
• Keywords: ALGORITHMICA 2010, Cyclic Preferences, Stable Matching Problem, Three-sided Stable Matching