An Algorithm for Multi-Attribute Diverse Matching

TL;DR

This paper introduces a novel combinatorial algorithm for maximizing diversity in bipartite b-matching problems, addressing multiple attributes simultaneously, and demonstrates its optimality and efficiency through theoretical and practical evaluations.

Contribution

It presents the first combinatorial algorithm for multi-attribute diversity maximization in b-matching, proving NP-hardness and offering a pseudo-polynomial time solution.

Findings

Algorithm guarantees optimal diverse matchings.

Method outperforms existing approaches in computational efficiency.

Successfully applied to reviewer assignment with improved diversity.

Abstract

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.