论鲁棒稳定婚姻的复杂性
On the Complexity of Robust Stable Marriage
摘要：
鲁棒稳定婚姻（英语：Robust Stable Marriage，简称RSM）是经典稳定婚姻问题的一个变种，其中给定稳定匹配的鲁棒性是通过在发生不可预见事件时修复它所需的修改次数来衡量的。我们专注于寻找（a，b）-超匹配的复杂性。（a，b）-超级匹配被定义为稳定匹配，其中如果任何“a”（非固定）男性/女性分手，则可以通过改变这些“a”男性/女性的伴侣以及最多“b”其他夫妇的伴侣来找到另一个稳定匹配。为了证明判定是否存在（a，b）-超匹配是NP-完全的，我们首先利用Schaefer的二分法引入了一个NP-完全的SAT公式。然后，我们证明了SAT公式和在特定的实例族上找到（1，1）-超匹配之间的等价性。
英文摘要：
Robust Stable Marriage (RSM) is a variant of the classical Stable Marriage problem, where the robustness of a given stable matching is measured by the number of modifications required for repairing it in case an unforeseen event occurs. We focus on the complexity of finding an (a,b)-supermatch. An (a,b)-supermatch is defined as a stable matching in which if any 'a' (non-fixed) men/women break up it is possible to find another stable matching by changing the partners of those 'a' men/women and also the partners of at most 'b' other couples. In order to show deciding if there exists an (a,b)-supermatch is NP-Complete, we first introduce a SAT formulation that is NP-Complete by using Schaefer's Dichotomy Theorem. Then, we show the equivalence between the SAT formulation and finding a (1,1)-supermatch on a specific family of instances.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
