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Optimal metric distortion for matching on the line
Journal article - Includes Student Work   Open access   Peer reviewed

Optimal metric distortion for matching on the line

Aris Filos-Ratsikas, Vasilis Gkatzelis, Mohamad Latifian, Emma Rewinski and Alexandros A Voudouris
Artificial intelligence, v 361, 104630
Dec 2026
DOI: https://doi.org/10.1016/j.artint.2026.104630
Featured in Collection :   Drexel's Newest Publications
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https://doi.org/10.1016/j.artint.2026.104630View
Published, Version of Record (VoR) Open Access via Drexel Libraries Read and Publish Program 2026 Open CC BY-NC-ND V4.0

Abstract

We study the distortion of one-sided and two-sided matching problems on the line. In the one-sided case, n agents need to be matched to n items, and each agent’s cost in a matching is their distance from the item they were matched to. We propose an algorithm that is provided only with ordinal information regarding the agents’ preferences (each agent’s ranking of the items from most- to least-preferred) and returns a matching aiming to minimize the social cost with respect to the agents’ true (cardinal) costs. We prove that our algorithm simultaneously achieves the best-possible approximation of 3 (known as distortion) with respect to a variety of social cost measures which include the utilitarian and egalitarian social cost. In the two-sided case, where the agents need be matched to n other agents and both sides report their ordinal preferences over each other, we show that it is always possible to compute an optimal matching. In fact, we show that this optimal matching can be achieved using even less information, and we provide bounds regarding the sufficient number of queries.

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