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Open AccessArticle

Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem

1
Instituto Nacional de Astrofísica, Óptica y Electrónica, Santa María Tonantzintla, Puebla 72840, Mexico
2
Consejo Nacional de Ciencia y Tecnología, Mexico City 03940, Mexico
3
Centro de Investigación en Computación del Instituto Politécnico Nacional, Mexico City 07738, Mexico
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1551; https://doi.org/10.3390/math8091551
Received: 11 August 2020 / Revised: 5 September 2020 / Accepted: 8 September 2020 / Published: 10 September 2020
(This article belongs to the Special Issue Evolutionary Computation and Mathematical Programming 2020)
The capacitated vertex k-center problem receives as input a complete weighted graph and a set of capacity constraints. Its goal is to find a set of k centers and an assignment of vertices that does not violate the capacity constraints. Furthermore, the distance from the farthest vertex to its assigned center has to be minimized. The capacitated vertex k-center problem models real situations where a maximum number of clients must be assigned to centers and the travel time or distance from the clients to their assigned center has to be minimized. These centers might be hospitals, schools, police stations, among many others. The goal of this paper is to explicitly state how the capacitated vertex k-center problem and the minimum capacitated dominating set problem are related. We present an exact algorithm that consists of solving a series of integer programming formulations equivalent to the minimum capacitated dominating set problem over the bottleneck input graph. Lastly, we present an empirical evaluation of the proposed algorithm using off-the-shelf optimization software. View Full-Text
Keywords: facility location; graph theory; integer programming; optimization facility location; graph theory; integer programming; optimization
MDPI and ACS Style

Cornejo Acosta, J.A.; García Díaz, J.; Menchaca-Méndez, R.; Menchaca-Méndez, R. Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem. Mathematics 2020, 8, 1551. https://doi.org/10.3390/math8091551

AMA Style

Cornejo Acosta JA, García Díaz J, Menchaca-Méndez R, Menchaca-Méndez R. Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem. Mathematics. 2020; 8(9):1551. https://doi.org/10.3390/math8091551

Chicago/Turabian Style

Cornejo Acosta, José A.; García Díaz, Jesús; Menchaca-Méndez, Ricardo; Menchaca-Méndez, Rolando. 2020. "Solving the Capacitated Vertex K-Center Problem through the Minimum Capacitated Dominating Set Problem" Mathematics 8, no. 9: 1551. https://doi.org/10.3390/math8091551

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