具有群体公平约束的匹配：在线和离线算法
Matchings with Group Fairness Constraints: Online and Offline Algorithms
摘要：
我们考虑的问题分配项目的平台存在组公平性约束。在输入中，每个项目都属于一定的类别，在本文中称为类。每个平台通过它可以从每个类服务的项目数量的上限来指定组公平性约束。此外，每个平台也有一个上限的项目，它可以服务的总数。目标是将项目分配到平台，以便在满足每个类的上限的同时最大化分配的项目数量。在某些情况下，有一个与匹配项目到平台相关联的收入，那么目标是最大化所产生的收入。这个问题模型的几个重要的现实世界中的问题，如广告拍卖，调度，资源分配，学校的选择等，我们还显示了一个有趣的连接计算广义最大独立集超图和排名项目组公平性约束。我们表明，如果类是任意的，那么问题是NP-困难的，并具有很强的不可逼近性。我们认为，在在线和离线设置下的类的自然限制的问题。在这些限制下，问题仍然是NP难的，但承认近似算法与小的近似因子。我们还实现了一些算法。我们的实验表明，该算法在实践中工作得很好，无论是在效率和被分配到一些平台的项目的数量。
英文摘要：
We consider the problem of assigning items to platforms in the presence of group fairness constraints. In the input, each item belongs to certain categories, called classes in this paper. Each platform specifies the group fairness constraints through an upper bound on the number of items it can serve from each class. Additionally, each platform also has an upper bound on the total number of items it can serve. The goal is to assign items to platforms so as to maximize the number of items assigned while satisfying the upper bounds of each class. In some cases, there is a revenue associated with matching an item to a platform, then the goal is to maximize the revenue generated. This problem models several important real-world problems like ad-auctions, scheduling, resource allocations, school choice etc.We also show an interesting connection to computing a generalized maximum independent set on hypergraphs and ranking items under group fairness constraints. We show that if the classes are arbitrary, then the problem is NP-hard and has a strong inapproximability. We consider the problem in both online and offline settings under natural restrictions on the classes. Under these restrictions, the problem continues to remain NP-hard but admits approximation algorithms with small approximation factors. We also implement some of the algorithms. Our experiments show that the algorithms work well in practice both in terms of efficiency and the number of items that get assigned to some platform.
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。
