TY - JOUR
T1 - Approximation Algorithms for the Vertex K-Center Problem
T2 - Survey and Experimental Evaluation
AU - Garcia-DIaz, Jesus
AU - Menchaca-Mendez, Rolando
AU - Menchaca-Mendez, Ricardo
AU - Pomares Hernandez, Saul
AU - Perez-Sansalvador, Julio Cesar
AU - Lakouari, Noureddine
N1 - Publisher Copyright:
© 2013 IEEE.
PY - 2019
Y1 - 2019
N2 - The vertex k-center problem is a classical NP-Hard optimization problem with application to Facility Location and Clustering among others. This problem consists in finding a subset C ⫅ V of an input graph G = (V, E), such that the distance from the farthest vertex in V to its nearest center in C is minimized, where iCi <; k, with k ϵ Z± as part of the input. Many heuristics, metaheuristics, approximation algorithms, and exact algorithms have been developed for this problem. This paper presents an analytical study and experimental evaluation of the most representative approximation algorithms for the vertex k-center problem. For each of the algorithms under consideration and using a common notation, we present proofs of their corresponding approximation guarantees as well as examples of tight instances of such approximation bounds, including a novel tight example for a 3-approximation algorithm. Lastly, we present the results of extensive experiments performed over de facto benchmark data sets for the problem which includes instances of up to 71009 vertices.
AB - The vertex k-center problem is a classical NP-Hard optimization problem with application to Facility Location and Clustering among others. This problem consists in finding a subset C ⫅ V of an input graph G = (V, E), such that the distance from the farthest vertex in V to its nearest center in C is minimized, where iCi <; k, with k ϵ Z± as part of the input. Many heuristics, metaheuristics, approximation algorithms, and exact algorithms have been developed for this problem. This paper presents an analytical study and experimental evaluation of the most representative approximation algorithms for the vertex k-center problem. For each of the algorithms under consideration and using a common notation, we present proofs of their corresponding approximation guarantees as well as examples of tight instances of such approximation bounds, including a novel tight example for a 3-approximation algorithm. Lastly, we present the results of extensive experiments performed over de facto benchmark data sets for the problem which includes instances of up to 71009 vertices.
KW - Approximation algorithms
KW - k-center problem
KW - polynomial time heuristics
UR - http://www.scopus.com/inward/record.url?scp=85091345650&partnerID=8YFLogxK
U2 - 10.1109/ACCESS.2019.2933875
DO - 10.1109/ACCESS.2019.2933875
M3 - Artículo
AN - SCOPUS:85091345650
SN - 2169-3536
VL - 7
SP - 109228
EP - 109245
JO - IEEE Access
JF - IEEE Access
M1 - 8792058
ER -