2026-07-22T06:21:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:25381 2026-03-19T13:04:17Z ddc:004 open_access

Smoothed Analysis of Online Metric Matching with a Single Sample: Beyond Metric Distortion Li, Yingxi Vitercik, Ellen Yang, Mingwei Online algorithm Metric matching Competitive analysis Smoothed analysis In the online metric matching problem, n servers and n requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available server, incurring a cost equal to their distance. The goal is to minimize the total matching cost. We study this problem in [0, 1]^d with the Euclidean metric, when servers are adversarial and requests are independently drawn from distinct distributions that satisfy a mild smoothness condition. Our main result is an O(1)-competitive algorithm for d ≠ 2 that requires no distributional knowledge, relying only on a single sample from each request distribution. To our knowledge, this is the first algorithm to achieve an o(log n) competitive ratio for non-trivial metrics beyond the i.i.d. setting. Our approach bypasses the Ω(log n) barrier introduced by probabilistic metric embeddings: instead of analyzing the embedding distortion and the algorithm separately, we directly bound the cost of the algorithm on the target metric space of a simple deterministic embedding. We then combine this analysis with lower bounds on the offline optimum for Euclidean metrics, derived via majorization arguments, to obtain our guarantees. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Yingxi Li and Ellen Vitercik and Mingwei Yang 2026 Is Part Of LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2026.94 urn:nbn:de:0030-drops-253815 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.94 eng https://creativecommons.org/licenses/by/4.0/legalcode