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arXiv · 2007.09079

Necessarily Optimal One-Sided Matchings

Hadi Hosseini·Vijay Menon·Nisarg Shah·Sujoy Sikdar
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Abstract

We study the classical problem of matching $n$ agents to $n$ objects, where the agents have ranked preferences over the objects. We focus on two popular desiderata from the matching literature: Pareto optimality and rank-maximality. Instead of asking the agents to report their complete preferences, our goal is to learn a desirable matching from partial preferences, specifically a matching that is necessarily Pareto optimal (NPO) or necessarily rank-maximal (NRM) under any completion of the partial preferences. We focus on the top-$k$ model in which agents reveal a prefix of their preference rankings. We design efficient algorithms to check if a given matching is NPO or NRM, and to check whether such a matching exists given top-$k$ partial preferences. We also study online algorithms for eliciting partial preferences adaptively, and prove bounds on their competitive ratio.

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Hadi Hosseini, Vijay Menon, Nisarg Shah, Sujoy Sikdar. 2020-07-17. Necessarily Optimal One-Sided Matchings. https://arxiv.org/abs/2007.09079

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