使稳定匹配适应不断变化的偏好
Adapting Stable Matchings to Evolving Preferences
摘要：
适应不断变化的环境和限制是现代社会成功的关键。我们通过提出稳定婚姻和稳定室友的“增量版本”来解决这个问题。也就是说，我们试图回答以下问题：对于这两个问题，什么是适应现有的稳定匹配的计算成本后，一些代理的偏好已经改变。在这样做的同时，我们还建模的约束，新的稳定匹配不应太不同于旧的。在形式化这些增量版本之后，我们提供了增量稳定婚姻和增量稳定室友的计算复杂性景观的相当全面的图片。为此，我们利用参数“变化程度”在输入（旧的和新的偏好配置文件之间的差异）和输出（旧的和新的稳定匹配之间的差异）。我们得到的硬度和易处理性的结果，特别是显示一个固定参数的易处理性的结果相对于参数“新旧稳定匹配之间的距离”。
英文摘要：
Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters "degree of change" both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter "distance between old and new stable matching".
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。
