A Fire Fighter’s Problem

Authors Rolf Klein, Elmar Langetepe, Christos Levcopoulos

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Rolf Klein
Elmar Langetepe
Christos Levcopoulos

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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)


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.
  • Motion Planning
  • Dynamic Environments
  • Spiralling strategies
  • Lower and upper bounds


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