TY - GEN

T1 - On the bounded-hop range assignment problem

AU - Carmi, Paz

AU - Chaitman-Yerushalmi, Lilach

AU - Trabelsi, Ohad

N1 - Funding Information:
The research is partially supported by the Lynn and William Frankel Center for Computer Science and by grant 680/11 from the Israel Science Foundation (ISF).
Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We study the problem of assigning transmission ranges to radio stations in the plane such that any pair of stations can communicate within a bounded number of hops h and the cost of the network is minimized. The cost of transmitting in a range r is proportional to rα, where α ≥ 1. We consider two settings of this problem: collinear station locations and arbitrary locations. For the case of collinear stations, we introduce the pioneer polynomial-time exact algorithm for any α ≥ 1 and constant h, and thus conclude that the 1D version of the problem, where h is a constant, is in P. For an arbitrary h, not necessarily a constant, and α = 1, we propose a 1.5-approximation algorithm. This improves the previously best known approximation ratio of 2. For the case of stations placed arbitrarily in the plane, we present a (6 + ε)-approximation algorithm, for any ε > 0. This improves the previously best known approximation ratio of 4(9h−2)/(h√ 2−1). Moreover, we show a (1.5+ε)-approximation algorithm for a case where deviation of one hop (h + 1 hops in total) is acceptable.

AB - We study the problem of assigning transmission ranges to radio stations in the plane such that any pair of stations can communicate within a bounded number of hops h and the cost of the network is minimized. The cost of transmitting in a range r is proportional to rα, where α ≥ 1. We consider two settings of this problem: collinear station locations and arbitrary locations. For the case of collinear stations, we introduce the pioneer polynomial-time exact algorithm for any α ≥ 1 and constant h, and thus conclude that the 1D version of the problem, where h is a constant, is in P. For an arbitrary h, not necessarily a constant, and α = 1, we propose a 1.5-approximation algorithm. This improves the previously best known approximation ratio of 2. For the case of stations placed arbitrarily in the plane, we present a (6 + ε)-approximation algorithm, for any ε > 0. This improves the previously best known approximation ratio of 4(9h−2)/(h√ 2−1). Moreover, we show a (1.5+ε)-approximation algorithm for a case where deviation of one hop (h + 1 hops in total) is acceptable.

UR - http://www.scopus.com/inward/record.url?scp=84951828938&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-21840-3_12

DO - 10.1007/978-3-319-21840-3_12

M3 - Conference contribution

AN - SCOPUS:84951828938

SN - 9783319218397

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

SP - 140

EP - 151

BT - Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings

A2 - Dehne, Frank

A2 - Sack, Jorg-Rudiger

A2 - Stege, Ulrike

PB - Springer Verlag

T2 - 14th International Symposium on Algorithms and Data Structures, WADS 2015

Y2 - 5 August 2015 through 7 August 2015

ER -