当前位置: X-MOL 学术Data Min. Knowl. Discov. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Fair-by-design matching
Data Mining and Knowledge Discovery ( IF 4.8 ) Pub Date : 2020-02-04 , DOI: 10.1007/s10618-020-00675-y
David García-Soriano , Francesco Bonchi

Matching algorithms are used routinely to match donors to recipients for solid organs transplantation, for the assignment of medical residents to hospitals, record linkage in databases, scheduling jobs on machines, network switching, online advertising, and image recognition, among others. Although many optimal solutions may exist to a given matching problem, when the elements that shall or not be included in a solution correspond to individuals, it becomes of paramount importance that the solution is selected fairly. In this paper we study individual fairness in matching problems. Given that many maximum matchings may exist, each one satisfying a different set of individuals, the only way to guarantee fairness is through randomization. Hence we introduce the distributional maxmin fairness framework which provides, for any given input instance, the strongest guarantee possible simultaneously for all individuals in terms of satisfaction probability (the probability of being matched in the solution). Specifically, a probability distribution over feasible solutions is maxmin-fair if it is not possible to improve the satisfaction probability of any individual without decreasing it for some other individual which is no better off. Our main contribution is a polynomial-time algorithm building on techniques from minimum cuts, and edge-coloring algorithms for regular bipartite graphs, and transversal theory. In the special case of bipartite matching, our algorithm runs in \(O((|V|^2 + |E| |V|^{2/3})\cdot (\log |V|)^2)\) expected time. An experimental evaluation of our fair-matching algorithm shows its ability to scale to graphs with tens of millions of vertices and hundreds of millions of edges, taking only a few minutes on a simple architecture. To the best of our knowledge, this yields the first large-scale implementation of the egalitarian mechanism of Bogomolnaia and Moulin (Econometrica 72(1):257–279, 2004). Our analysis confirms that our method provides stronger satisfaction probability guarantees than non-trivial baselines.

中文翻译:

设计公平匹配

匹配算法通常用于将供体与受体进行匹配,以进行实体器官移植,将医疗居民分配给医院,在数据库中记录链接,在机器上安排工作,网络切换,在线广告和图像识别等。尽管对于给定的匹配问题可能存在许多最佳解决方案,但是当解决方案中应包含或不包含的元素与个人相对应时,公平地选择解决方案就变得至关重要。在本文中,我们研究匹配问题中的个体公平。考虑到可能存在许多最大匹配,每个最大匹配都满足一组不同的个体,所以保证公平的唯一方法是通过随机化。因此,我们介绍了分布最大最小值公平性为任何给定的输入实例提供框架的框架,该框架可以同时为所有个体提供最大的满意满意度(在解决方案中被匹配的概率)。具体来说,如果不可能提高任何个体的满意概率而不降低其他个体的满意度,那么在可行解上的概率分布就是最大最小公平的。我们的主要贡献是基于最小割的技术,正则二部图的边着色算法和横向理论的多项式时间算法。在二分匹配的特殊情况下,我们的算法在\(O((| V | ^ 2 + | E | | V | ^ {2/3})\ cdot(\ log | V |)^ 2)\)中运行预计时间。对我们的公平匹配算法进行的实验评估表明,它能够缩放为具有数千万个顶点和数亿个边的图形,而在一个简单的体系结构上只需几分钟。据我们所知,这首次实现了波哥大尼亚和红磨坊的均等机制的首次大规模实施(Econometrica 72(1):257-279,2004)。我们的分析证实,与非平凡基准相比,我们的方法提供了更强的满意概率保证。
更新日期:2020-02-04
down
wechat
bug