Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Brunner, Josh; Wellman, Julian https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-127693
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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


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