Illuminating Both Sides of Line Segments

Abstract

What is the minimum number of light sources that can collectively illuminate both sides of n disjoint line segments in the plane? We prove that this optimization problem is NP-hard. The worst case analysis shows, however, that ⌊4(n + 1)/5⌋ light sources are always enough and sometimes necessary for all n ≥2.This problem was motivated by an open problem posed by Czyzowicz et al.: what is the minimal number of light sources that can collectively illuminate any set of n disjoint segments from one side at least.KeywordsLight SourceLine SegmentOpen ProblemProblem ComplexityComputer GraphicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.