  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 $t$ the total
length of all barriers built so far must not exceed $t \cdot v$, where $v$ is a
speed constant. How large a speed $v$ is needed? He proved that speed $v>2$ is
sufficient, and that $v>1$ is necessary. This gap of $(1,2]$ 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 $L_1$
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 $v=1.8772$ is sufficient,
while $v >1.66$ is necessary.
