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arXiv 1909.03350cs.AIcs.DS
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一种多属性差异匹配算法

An Algorithm for Multi-Attribute Diverse Matching

University of Maryland(马里兰大学);Northwestern University(西北大学)

Saba Ahmadi, Faez Ahmed, John P. Dickerson, Mark Fuge, Samir Khuller

摘要:

二分b-匹配,即市场一侧的代理与另一侧的一个或多个代理或项目匹配,是一种经典模型,用于无数应用领域,如医疗保健,广告,教育和一般资源分配。传统上,这种模型的主要目标是最大化组成匹配的线性函数(例如,线性社会福利最大化)。最近的工作研究了一个新的目标,平衡整体匹配的多样性和经济效率,其中的目标,而不是一个单调的子模函数的匹配。这个问题的基本版本可以在多项式时间内求解。在这项工作中,我们证明了同时最大化沿着几个特征的多样性的问题(例如,国籍,性别,技能)是NP难的。为了解决这个问题,我们开发了第一个组合算法,在伪多项式时间构造可证明最优的不同的b-匹配。我们还提供了一个混合二次配方相同的问题,并表明,我们的方法保证最佳的解决方案,并需要更少的计算时间的评审员分配应用程序。

英文摘要:

Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. Traditionally, the primary goal of such models is to maximize a linear function of the constituent matches (e.g., linear social welfare maximization) subject to some constraints. Recent work has studied a new goal of balancing whole-match diversity and economic efficiency, where the objective is instead a monotone submodular function over the matching. Basic versions of this problem are solvable in polynomial time. In this work, we prove that the problem of simultaneously maximizing diversity along several features (e.g., country of citizenship, gender, skills) is NP-hard. To address this problem, we develop the first combinatorial algorithm that constructs provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide a Mixed-Integer Quadratic formulation for the same problem and show that our method guarantees optimal solutions and takes less computation time for a reviewer assignment application.

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。

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