Three Persons Satisfactory Roommates Problem

Abstract

The Satisfactory Roommates Problem (SFRP) is the problem of finding satisfactory matching between any pair of roommates. In the SFRP, each person in the set of even cardinality 2n rank the 2n-1 others in order of preference. The satisfactory matching is the partition of the set into 2n/2 pairs of roommates based on the individual satisfactory level. In this Three Person Satisfactory Roommates Problem (TPSRP), there are 3n persons with a preference lists for each person for their two partners will be given.  Every person in the set could be ranked other (3n-1) members in the order of preference. A matching is defined to be a set of triples. This paper provides a new elaborated algorithm for finding a perfect triples in the rooms.