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It is shown that every simple polygon in general position with n walls can be illuminated from a single point light source s after at most (n-2)/4 diffuse reflections, and this bound is the best possible. A point s with this property can be computed in O(n n) time. It is also shown that the minimum number of diffuse reflections needed to illuminate a given simple polygon from a single point can be approximated up to an additive constant in polynomial time.arXiv:1402.5303v3 fatcat:smocfjusmncmppedcbgivmufwq