2026-09-10T09:44:33Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27746 2026-09-09T12:19:36Z ddc:004 open_access

Incremental Consistent k-Center Clustering Grilnberger, Mara Skarlatos, Antonis Consistent Clustering k-Center Dynamic Algorithms In the incremental consistent k-center clustering problem, we are given a sequence of adversarial point insertions and aim to maintain a k-center solution with small approximation ratio and small recourse. In this work, we explore the following question: what is the best approximation ratio of a polynomial-time algorithm with a worst-case recourse of 1? Our result improves upon the 6-approximation algorithm of Forster and Skarlatos [SODA '25], which itself improved over the 8-approximation algorithm of Charikar, Chekuri, Feder, and Motwani [STOC '97]. Moreover, we show that any incremental k-center algorithm that achieves an approximation ratio strictly less than √ 2 requires a worst-case recourse of k. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Mara Grilnberger and Antonis Skarlatos 2026 Is Part Of LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2026.29 urn:nbn:de:0030-drops-277466 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.29 eng https://creativecommons.org/licenses/by/4.0/legalcode