NP-Hardness of the Problem of Optimal Box Positioning

被引：0
|
作者：
Galatenko, Alexei, V [1 ]
Nersisyan, Stepan A. [1 ]
Zhuk, Dmitriy N. [1 ]
机构：
[1] Lomonosov Moscow State Univ, Fac Mech & Math, Leninskie Gory 1, Moscow 119991, Russia
来源：
MATHEMATICS | 2019年 / 7卷 / 08期
基金：
俄罗斯科学基金会;
关键词：
optimal box positioning; NP-hardness; computational geometry;
D O I：
10.3390/math7080711
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 subset of Rd, 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.
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页数：6
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