Almost Stable Matchings by Truncating the Gale–Shapley Algorithm
We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about t...
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| Vydané v: | Algorithmica Ročník 58; číslo 1; s. 102 - 118 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
Springer-Verlag
01.09.2010
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| ISSN: | 0178-4617, 1432-0541 |
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| Abstract | We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds.
We apply our results to give a distributed (2+
ε
)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching. |
|---|---|
| AbstractList | We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose–accept rounds executed by the Gale–Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at an almost stable matching even without full information about the problem instance; for each participant, knowing only its local neighbourhood is enough. In distributed-systems parlance, this means that if each person has only a constant number of acceptable partners, an almost stable matching emerges after a constant number of synchronous communication rounds.
We apply our results to give a distributed (2+
ε
)-approximation algorithm for maximum-weight matching in bicoloured graphs and a centralised randomised constant-time approximation scheme for estimating the size of a stable matching. |
| Author | Kaski, Petteri Floréen, Patrik Suomela, Jukka Polishchuk, Valentin |
| Author_xml | – sequence: 1 givenname: Patrik surname: Floréen fullname: Floréen, Patrik organization: Helsinki Institute for Information Technology HIIT, University of Helsinki – sequence: 2 givenname: Petteri surname: Kaski fullname: Kaski, Petteri organization: Helsinki Institute for Information Technology HIIT, University of Helsinki – sequence: 3 givenname: Valentin surname: Polishchuk fullname: Polishchuk, Valentin email: valentin.polishchuk@cs.helsinki.fi organization: Helsinki Institute for Information Technology HIIT, University of Helsinki – sequence: 4 givenname: Jukka surname: Suomela fullname: Suomela, Jukka organization: Helsinki Institute for Information Technology HIIT, University of Helsinki |
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| Cites_doi | 10.1137/S0097539793254571 10.1016/0020-0190(84)90025-5 10.1016/S0304-3975(99)00125-5 10.1007/BF02136029 10.1109/ICDCS.2009.69 10.1016/j.tcs.2007.04.040 10.1007/BF01935367 10.1109/FOCS.2008.81 10.1007/11671411_1 10.2307/2938326 10.1007/11780823_10 10.1016/0304-3975(94)90042-6 10.1007/s00182-007-0081-6 10.1002/net.3230130404 10.1287/moor.28.1.103.14256 10.1007/BF02219230 10.1109/ISTCS.1995.377023 10.1145/1109557.1109666 10.1007/978-3-540-93980-1_2 10.2307/2312726 10.1137/0221015 10.1002/9781118032718 10.1080/00029890.1962.11989827 10.1007/978-3-540-87779-0_6 10.1007/11774129 10.1007/978-3-540-24596-4_7 10.1007/978-3-540-30186-8_24 |
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| Keywords | Distributed stable matching Local algorithms Constant-time randomised algorithms Almost stable matching |
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| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation |
| Title | Almost Stable Matchings by Truncating the Gale–Shapley Algorithm |
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