TY - GEN

T1 - On the minimum cost range assignment problem

AU - Carmi, Paz

AU - Chaitman-Yerushalmi, Lilach

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84951998400&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-48971-0_9

DO - 10.1007/978-3-662-48971-0_9

M3 - Conference contribution

AN - SCOPUS:84951998400

SN - 9783662489703

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 95

EP - 105

BT - Algorithms and Computation - 26th International Symposium, ISAAC 2015, Proceedings

A2 - Elbassioni, Khaled

A2 - Makino, Kazuhisa

PB - Springer Verlag

T2 - 26th International Symposium on Algorithms and Computation, ISAAC 2015

Y2 - 9 December 2015 through 11 December 2015

ER -