Algorithms for Super Stable Matching and Strongly Stable Matching

• Main Authors: Lin, I-Ming, 林義明
• Other Authors: Jimmy J. M. Tan
• Format: Others
• Language: zh-TW
• Published: 1996
• Online Access: http://ndltd.ncl.edu.tw/handle/15909480852057729966

碩士 === 國立交通大學 === 資訊科學學系 === 84 === An instaance of the classical stable marriage problem is that of matching n mem and n women, each of whom has ranked the members of the opposite sex in strict order of preference, so that no unmatched couple both prefer each otherto their partners under the matching. For every stable marriage instance, thereexists at least one stable matching, and there is an efficient algorithms forfinding such a matching. The stable roommates problem is that of matching a setof n persons into n/2 disjoint pairs, each member of them ranks all the others in strict order of preference. A stable matching is one that no two unmatchedmembers both prefer each other to their partners under the matching. There is no guarantee that stable matchings exist in this case. In the classical versionof these two problems, each person must rank the members of the others in strict order of preference. If preference list allows indifferent, so that aperson may have ties in his/her preference list, the definition of stablity may be generalized in three ways, namely weakly stablity, strong stablity andsuper stablity. The question of finding weakly stable matching for roommatesproblem is NP- complete. In this paper, we describe algirithms to find whether astable matching exists in strong stablity and super stablity cases for roomates problem, and if so, it will find such a matching.