1 research outputs found
Geometric Firefighting in the Half-plane
In 2006, Alberto Bressan suggested the following problem. Suppose a circular
fire spreads in the Euclidean plane at unit speed. The task is to build, in
real time, barrier curves to contain the fire. At each time the total
length of all barriers built so far must not exceed , where is a
speed constant. How large a speed is needed? He proved that speed is
sufficient, and that is necessary. This gap of is still open. The
crucial question seems to be the following. {\em When trying to contain a fire,
should one build, at maximum speed, the enclosing barrier, or does it make
sense to spend some time on placing extra delaying barriers in the fire's way?}
We study the situation where the fire must be contained in the upper
half-plane by an infinite horizontal barrier to which vertical line segments
may be attached as delaying barriers. Surprisingly, such delaying barriers are
helpful when properly placed. We prove that speed is sufficient,
while is necessary.Comment: 15 pages, 10 figures, pre-print of an article published in WADS 201