Three Persons Satisfactory Roommates Problem with Ties, Ties and Incomplete List

Abstract

Solving the Satisfactory Roommates Problem (SFRP) involves determining a satisfactory match between any two roommates. Every member of the set of even cardinality ranks the other members in order of preference in the SFRP. The division of the set into roommate pairs according to each person's satisfactory level is known as satisfactory matching. The satisfactory roommates' problem (SFRP) is generalized to a new level where preference lists with ties, ties, and incomplete lists are present. There are 3n individuals in this Three person Satisfactory Roommates Problem (TPSRP), and each individual has preference lists for their two companions. Less than with ties is preferred by certain people. We use the TPSR algorithm to identify suitable matching, which is based on preference value and helps determine satisfactory matching of roommates problem with ties (TPSRT), ties and incomplete list (TPSRTI). A new, complex algorithm for finding perfect triples in rooms is presented in this study.