Abstract
Given two compact convex sets C 1 and C 2 in the plane, we consider the problem of finding a placement ϕC 1 of C 1 that minimizes the area of the convex hull of ϕC 1 ∪ C 2. We first consider the case where ϕC 1 and C 2 are allowed to intersect (as in “stacking” two flat objects in a convex box), and then add the restriction that their interior has to remain disjoint (as when “bundling” two convex objects together into a tight bundle). In both cases, we consider both the case where we are allowed to reorient C 1, and where the orientation is fixed. In the case without reorientations, we achieve exact near-linear time algorithms, in the case with reorientations we compute a (1 + ε)-approximation in time O(ε − 1/2 log n + ε − 3/2 log ε − 1/2), if two sets are convex polygons with n vertices in total.
This research was supported by LG Electronics.
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Ahn, HK., Cheong, O. (2005). Stacking and Bundling Two Convex Polygons. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_88
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DOI: https://doi.org/10.1007/11602613_88
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