# Parallel Algorithm for Finding the Smallest Enclosing Rectangle on SIMD Machines

May 11th, 2015
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In this thesis, we present a parallel algorithm for nding the smallest enclosing rectangle which encloses a set S of n points in the plane. This problem arises frequently in industrial elds such as packing and optimal layout problems. Using the property that the smallest enclosing rectangle of a convex hull for S has the same area as that of n points in S , we rst compute a convex hull for S and then nd the smallest enclosing rectangle directly from that convex hull.

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Recommendation ReportParallel Algorithm for Finding the Smallest Enclosing Rectangle on SIMD MachinesJung-Ju Choi Department of Computer Science POSTECH P.O. Box 125, Pohang 790-600, KOREA.AbstractIn this thesis, we present a parallel algorithm for nding the smallest enclosing rectangle which encloses a set S of n points in the plane. This problem arises frequently in industrial elds such as packing and optimal layout problems. Using the property that the smallest enclosing rectangle of a convex hull for S has the same area as that of n points in S , we rst compute a convex hull for S and then nd the smallest enclosing rectangle directly from that convex hull. Therefore, our algorithm can be executed very fast with small constant factor. The proposed algorithm can be generally implemented on SIMD (Single Instruction stream and Multiple Data stream)-type parallel computers such as MCC (Mesh Connected Computer) and CCC (Cube Connected Computer). Our parallel algorithm can be executed with the time complexity p O( n) and O(log n) on MCC and CCC respectively. 2Contents1 Introduction 2 Models of Parallel Computations2.1 Parallel Architecture : : : : 2.1.1 MCC : : : : : : : : : 2.1.2 CCC : : : : : : : : : 2.2 Problem Solving Technique : 2.3 Basic Parallel Operations : :1: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 8 9

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