有序世界中的真实匹配和聚类机制
Truthful Mechanisms for Matching and Clustering in an Ordinal World
摘要：
我们研究真实的匹配机制和相关问题的部分信息设置，代理人的真实效用是隐藏的，算法只能访问顺序偏好信息。我们的模型的动机是这样一个事实，即在许多情况下，代理不能表达他们的效用为不同的结果的数值，但仍然能够排名的结果，他们的偏好顺序。具体来说，我们研究的问题，地面真理存在的形式加权图的代理效用，但算法只能引出代理的私人信息的形式的优先顺序为每个代理引起的潜在的权重。在此背景下，我们设计了真实的算法来逼近隐藏权重的真正最优解。我们的技术产生普遍真实的算法的一些图的问题：1. 76-近似算法的最大权匹配，2-近似算法的最大k匹配，6-近似算法Denmark子图，和2-近似算法的最大旅行商，只要隐藏的权重构成一个度量。我们还提供了改进的近似算法这样的问题时，代理商是不能说谎，他们的喜好。我们的研究结果是第一个非平凡的真实近似算法，这些问题，并表明，在许多情况下，我们可以设计强大的算法，即使当代理可能会说谎，只提供序数信息，而不是精确的实用程序。
英文摘要：
We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the fact that in many settings, agents cannot express the numerical values of their utility for different outcomes, but are still able to rank the outcomes in their order of preference. Specifically, we study problems where the ground truth exists in the form of a weighted graph of agent utilities, but the algorithm can only elicit the agents' private information in the form of a preference ordering for each agent induced by the underlying weights. Against this backdrop, we design truthful algorithms to approximate the true optimum solution with respect to the hidden weights. Our techniques yield universally truthful algorithms for a number of graph problems: a 1.76-approximation algorithm for Max-Weight Matching, 2-approximation algorithm for Max k-matching, a 6-approximation algorithm for Densest k-subgraph, and a 2-approximation algorithm for Max Traveling Salesman as long as the hidden weights constitute a metric. We also provide improved approximation algorithms for such problems when the agents are not able to lie about their preferences. Our results are the first non-trivial truthful approximation algorithms for these problems, and indicate that in many situations, we can design robust algorithms even when the agents may lie and only provide ordinal information instead of precise utilities.
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。
