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Title of Journal: Algorithmica

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Abbravation: Algorithmica

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Springer-Verlag

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10.1007/978-3-642-78646-4

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1432-0541

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Aligning Two Convex Figures to Minimize Area or Pe

Authors: HeeKap Ahn Otfried Cheong
Publish Date: 2010/11/03
Volume: 62, Issue: 1-2, Pages: 464-479
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Abstract

Given two compact convex sets P and Q in the plane we consider the problem of finding a placement ϕ P of P that minimizes the convex hull of ϕ P∪Q We study eight versions of the problem we consider minimizing either the area or the perimeter of the convex hull we either allow ϕ P and Q to intersect or we restrict their interiors to remain disjoint and we either allow reorienting P or require its orientation to be fixed In the case without reorientations we achieve exact nearlinear time algorithms for all versions of the problem In the case with reorientations we compute a 1+εapproximation in time Oε −1/2log n+ε −3/2log  a 1/ε if the two sets are convex polygons with n vertices in total where a∈012 depending on the version of the problemHK Ahn was supported by the National Research Foundation of Korea Grant funded by the Korean Government MEST NRF20090067195 O Cheong was supported by Midcareer Researcher Program through NRF grant funded by the MEST No R012008000116070

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