1994
DOI: 10.1137/s0097539789169483
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A New Approach to Stable Matching Problems

Abstract: We show that Stable Matching problems are the same as problems about stable configurations of X-networks. Consequences include easy proofs of old theorems, a new simple algorithm for finding a stable matching, an understanding of the difference between Stable Marriage and Stable Roommates, NTcompleteness of Three-party Stable Marriage, CC-completeness of several Stable Matching problems, and a fast parallel reduction from the Stable Marriage problem to the ' Assignment problem.

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Cited by 64 publications
(45 citation statements)
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“…It has been proved in [13] that the problem of deciding whether a three-sided matching algorithm can reach stability is NP-complete. Thus, there may exist scenarios that a three-sided matching problem has no stable result.…”
Section: ) Stabilitymentioning
confidence: 99%
“…It has been proved in [13] that the problem of deciding whether a three-sided matching algorithm can reach stability is NP-complete. Thus, there may exist scenarios that a three-sided matching problem has no stable result.…”
Section: ) Stabilitymentioning
confidence: 99%
“…That is, is it the case that Alice and Bob are married to each other in some stable marriage? REFERENCE: Mayr and Subramanian [18], and Subramanian [29]. REMARKS: The reduction is from the CCVP [29].…”
Section: Lexicographically First Maximal Matching Problem (Lfmmp)mentioning
confidence: 99%
“…See also (Feder [26], Moore and Machta [27], Ramachandran and Wang [28], and Subramanian [29,30]) for more research on CC. Our discussion follows the format used by Greenlaw et al [19].…”
Section: A Compendium Of Cc-complete Problemsmentioning
confidence: 99%
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“…The paper Subramanian [1989] shows that this problem may be viewed as a problem about fanout-limited circuits with feedback. Consequences include putting this problem into the class CC (one of the classes defined in Mayr and Subramanian [1989]), thus giving evidence that this problem has intermediate difficulty of paralleization.…”
Section: Circuit-value Problems and Network Stability Problemsmentioning
confidence: 99%