2026-07-25T06:21:18Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:5104 2024-03-06T10:35:56Z ddc:004 open_access

A Fire Fighter’s Problem Klein, Rolf Langetepe, Elmar Levcopoulos, Christos Motion Planning Dynamic Environments Spiralling strategies Lower and upper bounds 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rolf Klein and Elmar Langetepe and Christos Levcopoulos 2015 Is Part Of LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SOCG.2015.768 urn:nbn:de:0030-drops-51044 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.768 eng https://creativecommons.org/licenses/by/3.0/legalcode