2026-07-23T03:46:27Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:12769 2024-03-06T10:49:08Z ddc:004 open_access

An Optimal Algorithm for Online Freeze-Tag Brunner, Josh Wellman, Julian Online algorithm competitive ratio freeze-tag In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online variant of the problem, each frozen robot is not revealed until a specified time. Hammar, Nilsson, and Persson have shown that no online algorithm can achieve a competitive ratio better than 7/3 for online freeze-tag, and posed the question of whether an O(1)-competitive algorithm exists. We provide a (1+√2)-competitive algorithm for online time-dependent freeze-tag, and show that this is the best possible: there does not exist an algorithm which achieves a lower competitive ratio on every metric space. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Josh Brunner and Julian Wellman 2020 Is Part Of LIPIcs, Volume 157, 10th International Conference on Fun with Algorithms (FUN 2021) (2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FUN.2021.8 urn:nbn:de:0030-drops-127693 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2021.8 eng https://creativecommons.org/licenses/by/3.0/legalcode