TY - GEN
T1 - A Fire Fighter's Problem.
AU - Klein, Rolf
AU - Langetepe, Elmar
AU - Levcopoulos, Christos
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Motion Planning
KW - Dynamic Environments
KW - Spiralling strategies
KW - Lower and upper bounds
U2 - 10.4230/LIPIcs.SOCG.2015.768
DO - 10.4230/LIPIcs.SOCG.2015.768
M3 - Paper in conference proceeding
VL - 34
SP - 768
EP - 780
BT - Leibniz International Proceedings in Informatics (LIPIcs)
A2 - Arge, Lars
A2 - Pach, Janos
PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik
T2 - 31st International Symposium on Computational Geometry (SoCG 2015)
Y2 - 22 June 2015
ER -