Ashish Sabharwal ,
Atri Rudra and Erik Vee
Floodlight Illumination of Infinite Wedges
The floodlight illumination problem asks whether there exists a
one-to-one placement of n floodlights illuminating infinite wedges
of angles a1,...,an at n sites p1,...,
pn in a plane such that a given infinite wedge
W of angle q
located at point q is completely illuminated by the floodlights. We
prove that this problem is NP-hard, closing an open problem from 2001.
In fact, we show that the problem is NP-complete
even when ai =
a for all 1£
i £ n (the
uniform case) and q =
n (the tight
case). On the positive side, we describe sufficient conditions on the
sites of floodlights for which there are efficient algorithms
to find an illumination. We discuss various approximate solutions and
show that computing any finite approximation is NP-hard while
e-angle approximations can be obtained efficiently.
- Abstract in the 14th Annual Fall Workshop on Computational Geometry. November 2004.
- Full version submitted to Computation Geometry: Theory and Applications (CGTA). [PDF]