We study the problem of assigning transmission ranges to radio stations placed in a d-dimensional (d-D) Euclidean space in order to achieve a strongly connected communication network with minimum total cost, where the cost of transmitting in range r is proportional to rα. While this problem can be solved optimally in 1D, in higher dimensions it is known to be NP-hard for any α ≥ 1. For the 1D version of the problem and α ≥ 1, we propose a new approach that achieves an exact O(n2)-time algorithm. This improves the running time of the best known algorithm by a factor of n. Moreover, we show that this new technique can be utilized for achieving a polynomialtime algorithm for finding the minimum cost range assignment in 1D whose induced communication graph is a t-spanner, for any t ≥ 1. In higher dimensions, finding the optimal range assignment is NPhard; however, it can be approximated within a constant factor. The best known approximation ratio is for the case α = 1, where the approximation ratio is 1.5. We show a new approximation algorithm that breaks the 1.5 ratio.
CITATION STYLE
Carmi, P., & Chaitman-Yerushalmi, L. (2015). On the minimum cost range assignment problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9472, pp. 95–105). Springer Verlag. https://doi.org/10.1007/978-3-662-48971-0_9
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