Searching approximate global optimal Heilbronn configurations of nine points in the unit square via GPGPU computing

Liangyu Chen (), Yaochen Xu () and Zhenbing Zeng ()
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Liangyu Chen: East China Normal University
Yaochen Xu: East China Normal University
Zhenbing Zeng: Shanghai University

Journal of Global Optimization, 2017, vol. 68, issue 1, No 7, 147-167

Abstract: Abstract In this paper we present a method of applying the GPGPU technology to compute the approximate optimal solution to the Heilbronn problem for nine points in the unit square, namely, points $$P_1,P_2,\ldots ,P_9$$ P 1 , P 2 , … , P 9 in $$[0,1]\times [0,1]$$ [ 0 , 1 ] × [ 0 , 1 ] so that the minimal area of triangles $$P_iP_jP_k\,(1\le i

Keywords: Heilbronn problem; Rectangle partition; Branch-and-bound method; Combinatorial geometry; GPGPU technology (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-016-0453-1

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