What is the minimal number of light sources which is always sufficient to illuminate the plane in the presence of n disjoint opaque line segments? For n⩾5, O'Rourke proved that ⌊2n/3⌋ light sources are always sufficient and sometimes necessary, if light sources can be placed on the line segments and thus they can illuminate both sides of a segment.
We prove that ⌊2(n+1)/3⌋ light sources are always sufficient and sometimes necessary, if light sources cannot be placed on the line segments. An O(nlogn) time algorithm is presented which allocates at most ⌊2(n+1)/3⌋ light sources collectively illuminating the plane.
The author acknowledges support from the joint Berlin–Zürich graduate program “Combinatorics, Geometry, and Computation”, financed by the German Science Foundation (DFG) and ETH Zürich.