| Summary: | 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.
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