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Given a set P = {P0,. .. , P k−1 } of k convex polygons having n vertices in total in the plane, we consider the problem of finding k translations τ0,. .. , τ k−1 of P0,. .. , P k−1 such that the translated copies τiPi are pairwise disjoint and the area or the perimeter of the convex hull of k−1 i=0 τiPi is minimized. When k = 2, the problem can be solved… (More)

Given two convex d-polytopes P and Q in R d for d ≥ 3, we study the problem of bundling P and Q in a smallest convex container. More precisely, our problem asks to find a minimum convex set containing P and Q that are in contact under translations. For dimension d = 3, we present the first exact algorithm that runs in O(n 3) time, where n denotes the number… (More)

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