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NP-Hardness of the Problem of Optimal Box Positioning

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
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Mathematics 2019, 7(8), 711; https://doi.org/10.3390/math7080711
Received: 12 June 2019 / Revised: 2 August 2019 / Accepted: 4 August 2019 / Published: 6 August 2019
(This article belongs to the Section Mathematics and Computer Science)
We consider the problem of finding a position of a d-dimensional box with given edge lengths that maximizes the number of enclosed points of the given finite set P R d , i.e., the problem of optimal box positioning. We prove that while this problem is polynomial for fixed values of d, it is NP-hard in the general case. The proof is based on a polynomial reduction technique applied to the considered problem and the 3-CNF satisfiability problem. View Full-Text
Keywords: optimal box positioning; NP-hardness; computational geometry optimal box positioning; NP-hardness; computational geometry
MDPI and ACS Style

Galatenko, A.V.; Nersisyan, S.A.; Zhuk, D.N. NP-Hardness of the Problem of Optimal Box Positioning. Mathematics 2019, 7, 711. https://doi.org/10.3390/math7080711

AMA Style

Galatenko AV, Nersisyan SA, Zhuk DN. NP-Hardness of the Problem of Optimal Box Positioning. Mathematics. 2019; 7(8):711. https://doi.org/10.3390/math7080711

Chicago/Turabian Style

Galatenko, Alexei V., Stepan A. Nersisyan, and Dmitriy N. Zhuk 2019. "NP-Hardness of the Problem of Optimal Box Positioning" Mathematics 7, no. 8: 711. https://doi.org/10.3390/math7080711

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