Stable roommates and constraint programming

Abstract

In the stable roommates (SR) problem we have n agents, where each agent ranks all n-1 other agents. The problem is then to match agents into pairs such that no two agents prefer each other to their matched partners. A remarkably simple constraint encoding is presented that uses O(n2) binary constraints, and in which arc-consistency (the phase-1 table) is established in O(n3) time. This leads us to a specialized n-ary constraint that uses O(n) additional space and establishes arc-consistency in O(n2) time. This can model stable roommates with incomplete lists (SRI), consequently it can also model stable marriage (SM) problems with complete and incomplete lists (SMI). That is, one model suffices. An empirical study is performed and it is observed that the n-ary constraint model can read in, model and output all matchings for instances with n=1,000 in about 2 seconds on current hardware platforms. Enumerating all matchings is a crude solution to the egalitarian SR problem, and the empirical results suggest that although NP-hard, egalitarian SR is practically easy. © 2014 Springer International Publishing.