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Solving stable matching problems using answer set programming

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Abstract
Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed.
Keywords
Answer set programming, Logic rules, Stable marriage problem, Optimal stable matchings, KIDNEY EXCHANGE, MARRIAGE, ALGORITHMS

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Chicago
De Clercq, Sofie, Steven Schockaert, Martine De Cock, and Ann Nowé. 2016. “Solving Stable Matching Problems Using Answer Set Programming.” Theory and Practice of Logic Programming 16 (3): 247–268.
APA
De Clercq, Sofie, Schockaert, S., De Cock, M., & Nowé, A. (2016). Solving stable matching problems using answer set programming. THEORY AND PRACTICE OF LOGIC PROGRAMMING, 16(3), 247–268. Presented at the 8th International Web Rule symposium (RuleML) ; in conjunction with 21st European conference on Artificial Intelligence (ECAI).
Vancouver
1.
De Clercq S, Schockaert S, De Cock M, Nowé A. Solving stable matching problems using answer set programming. THEORY AND PRACTICE OF LOGIC PROGRAMMING. 2016;16(3):247–68.
MLA
De Clercq, Sofie, Steven Schockaert, Martine De Cock, et al. “Solving Stable Matching Problems Using Answer Set Programming.” THEORY AND PRACTICE OF LOGIC PROGRAMMING 16.3 (2016): 247–268. Print.
@article{7171798,
  abstract     = {Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed.},
  author       = {De Clercq, Sofie and Schockaert, Steven and De Cock, Martine and Now{\'e}, Ann},
  issn         = {1471-0684},
  journal      = {THEORY AND PRACTICE OF LOGIC PROGRAMMING},
  language     = {eng},
  location     = {Prague, Czech Republic},
  number       = {3},
  pages        = {247--268},
  title        = {Solving stable matching problems using answer set programming},
  url          = {http://dx.doi.org/10.1017/S147106841600003X},
  volume       = {16},
  year         = {2016},
}

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