Abstract
We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon P with n vertices. We give a randomized near-linear-time (1 − ϵ)-approximation algorithm for this problem: in O((n/ϵ6) log2 n log(1/δ)) time we find a convex polygon contained in P that, with probability at least 1 − δ, has area at least (1 − ϵ) times the area of an optimal solution.
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