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DOI: 10.4230/LIPIcs.FUN.2021.8
URN: urn:nbn:de:0030-drops-127693
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12769/
Brunner, Josh ; Wellman, Julian
An Optimal Algorithm for Online Freeze-Tag
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Abstract
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.
BibTeX - Entry
@InProceedings{brunner_et_al:LIPIcs:2020:12769,
author = {Josh Brunner and Julian Wellman},
title = {{An Optimal Algorithm for Online Freeze-Tag}},
booktitle = {10th International Conference on Fun with Algorithms (FUN 2021)},
pages = {8:1--8:11},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-145-0},
ISSN = {1868-8969},
year = {2020},
volume = {157},
editor = {Martin Farach-Colton and Giuseppe Prencipe and Ryuhei Uehara},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12769},
URN = {urn:nbn:de:0030-drops-127693},
doi = {10.4230/LIPIcs.FUN.2021.8},
annote = {Keywords: Online algorithm, competitive ratio, freeze-tag}
}
| Keywords: | Online algorithm, competitive ratio, freeze-tag | |
| Seminar: | 10th International Conference on Fun with Algorithms (FUN 2021) | |
| Issue date: | 2020 | |
| Date of publication: | 16.09.2020 |
