Covering a simplex by spheres: complexity and algorithms

Simplex covering optimization problem (SCO) is modeled from the application of covering a simplex by m given balls. It contains the maximin dispersion problem as a special case. In this paper, we prove that (SCO) is NP-hard. We present an enumeration method (EM) to globally solve (SCO) and show that...

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Bibliographic Details
Published in:Journal of global optimization Vol. 84; no. 1; pp. 119 - 135
Main Authors: Zhang, Tongli, Xia, Yong
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Analysis
Complexity
Computer Science
Enumeration
Experiments
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Real Functions
90C20
NP-hard
Maximin dispersion
90C26
90C47
Simplex covering
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:Simplex covering optimization problem (SCO) is modeled from the application of covering a simplex by m given balls. It contains the maximin dispersion problem as a special case. In this paper, we prove that (SCO) is NP-hard. We present an enumeration method (EM) to globally solve (SCO) and show that the complexity is strongly polynomial when m is fixed. Numerical experiments demonstrate that EM outperforms CPLEX when m is small. For larger m , we propose an efficient incomplete enumeration method based on linear programming relaxation.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01137-z