License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SOCG.2015.768
URN: urn:nbn:de:0030-drops-51044
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5104/
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Klein, Rolf ; Langetepe, Elmar ; Levcopoulos, Christos

A Fire Fighter’s Problem

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Abstract

Suppose that a circular fire spreads in the plane at unit speed. A fire fighter can build a barrier at speed v > 1. How large must v be to ensure that the fire can be contained, and how should the fire fighter proceed? We provide two results. First, we analyze the natural strategy where the fighter keeps building a barrier along the frontier of the expanding fire. We prove that this approach contains the fire if v > v_c = 2.6144... holds. Second, we show that any "spiralling" strategy must have speed v > 1.618, the golden ratio, in order to succeed.

BibTeX - Entry

@InProceedings{klein_et_al:LIPIcs:2015:5104,
  author =	{Rolf Klein and Elmar Langetepe and Christos Levcopoulos},
  title =	{{A Fire Fighter’s Problem}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{768--780},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Lars Arge and J{\'a}nos Pach},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5104},
  URN =		{urn:nbn:de:0030-drops-51044},
  doi =		{10.4230/LIPIcs.SOCG.2015.768},
  annote =	{Keywords: Motion Planning, Dynamic Environments, Spiralling strategies, Lower and upper bounds}
}

Keywords: Motion Planning, Dynamic Environments, Spiralling strategies, Lower and upper bounds
Collection: 31st International Symposium on Computational Geometry (SoCG 2015)
Issue Date: 2015
Date of publication: 12.06.2015

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