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. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

本文通过使用ASP编码，提出了一种能自由适应特定应用需求且具有高效率的算法来解决稳定婚姻问题，并且尝试基于用户需求选择最优匹配方案。此编码为首个能在考虑到指定不接受伴侣和允许多种匹配程度下找到完全符合性等、最小后悔和最大基数的SMP实例的精确实现， 该方法将会在TPLP上发表。

使用答案集编程解决稳定匹配问题