Abstract
Given a metric graph G = (V, E, w) and a center c ∈ V, and an integer k, the Star k-Hub Center Problem is to find a depth-2 spanning tree T of G rooted by c such that c has exactly k children and the diameter of T is minimized. Those children of c in T are called hubs. The Star k-Hub Center Problem is NP-hard. (Liang, Operations Research Letters, 2013) proved that for any ε > 0, it is NP-hard to approximate the Star k-Hub Center Problem to within a ratio 1.25 −ε. In the same paper, a 3.5-approximation algorithm was given for the Star k-Hub Center Problem. In this paper, we show that for any ε > 0, to approximate the Star k-Hub Center Problem to a ratio 1.5 − ε is NP-hard. Moreover, we give 2-approximation and 5/3-approximation algorithms for the same problem.
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CITATION STYLE
Chen, L. H., Cheng, D. W., Hsieh, S. Y., Hung, L. J., Lee, C. W., & Wu, B. Y. (2016). Approximation algorithms for the star k-hub center problem in metric graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9797, pp. 222–234). Springer Verlag. https://doi.org/10.1007/978-3-319-42634-1_18
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