We initiate the study of external manipulations in Stable Marriage by considering several manipulative actions as well as several "desirable" manipulation goals. For instance, one goal is to make sure that a given pair of agents is matched in a stable solution, and this may be achieved by the manipulative action of reordering some agents' preference lists. We present a comprehensive study of the computational complexity of all problems arising in this way. We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard cases, focusing on the natural parameter "budget" (that is, the number of manipulative actions), we also perform a parameterized complexity analysis and encounter parameterized hardness results.
翻译:我们开始研究稳定婚姻中的外部操纵行为,方法是考虑几种操纵行为以及若干“理想”操纵目标。例如,一个目标是确保一对特定物剂在稳定的解决方案中匹配,这可以通过重新排序某些物剂的偏好列表的操纵行动来实现。我们全面研究了由此产生的所有问题的计算复杂性。我们发现了几个多米时可溶性案例以及一些NP硬性案例。对于侧重于自然参数“预算”(即操纵行动的数量)的NP硬性案例,我们还进行了参数化的复杂性分析和遇到参数化硬性结果。