Conference proceeding
Optimal Metric Distortion for Matching on the Line
IJCAI (United States), pp 3857-3865
2025
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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Details
- Title
- Optimal Metric Distortion for Matching on the Line
- Creators
- Aris Filos-Ratsikas - University of EdinburghVasilis Gkatzelis - Drexel UniversityMohamad Latifian - University of EdinburghEmma Rewinski - Drexel UniversityAlexandros A. Voudouris - University of Essex
- Publication Details
- IJCAI (United States), pp 3857-3865
- Publisher
- International Joint Conferences on Artificial Intelligence
- Grant note
- Engineering and Physical Sciences Research Council (http://data.elsevier.com/vocabulary/SciValFunders/501100000266) CCF-2047907; CCF-2210502 / National Science Foundation (http://data.elsevier.com/vocabulary/SciValFunders/100000001) EP/Y003624/1 / Engineering and Physical Sciences Research Council (501100000266) National Science Foundation (http://data.elsevier.com/vocabulary/SciValFunders/100000001) CCF-2047907 / Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences (501100002902) EP/Y003624/1 / Engineering and Physical Sciences Research Council (http://data.elsevier.com/vocabulary/SciValFunders/501100000266) CCF-2210502 / National Sleep Foundation (100003187)
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- Computer Science (Computing)
- Scopus ID
- 2-s2.0-105021802877
- Other Identifier
- 991022133621504721