LIPIcs.SOCG.2015.768.pdf
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A Fire Fighter’s Problem
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31st International Symposium on Computational Geometry (SoCG 2015)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Computational Geometry (SoCG) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2015-06-12
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Rolf Klein, Elmar Langetepe, and Christos Levcopoulos. A Fire Fighter’s Problem. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 768-780, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.SOCG.2015.768
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.
Subject Classification
Keywords
- Motion Planning
- Dynamic Environments
- Spiralling strategies
- Lower and upper bounds
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