Wireless information networks
Optimal transmission ranges for mobile communication in linear multihop packet radio networks
Wireless Networks - Special issue on performance evaluation methods for wireless networks
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Dynamic channel allocation for linear macrocellular topology
Proceedings of the 1999 ACM symposium on Applied computing
Power Consumption in Packet Radio Networks (Extended Abstract)
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
The Power Range Assignment Problem in Radio Networks on the Plane
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
The Impact of Knowledge on Broadcasting Time in Radio Networks
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
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Given a set S of radio stations located on a line and an integer h (1 ≤ h ≤ |S| - 1), the Min Assignment problem is to find a range assignment of minimum power consumption provided that any pair of stations can communicate in at most h hops. Previous positive results for this problem were known only when h = |S| - 1 (i.e. the unbounded case) or when the stations are equally spaced (i.e. the uniform chain). In particular, Kirousis, Kranakis, Krizanc and Pelc (1997) provided an efficient exact solution for the unbounded case and efficient approximated solutions for the uniform chain, respectively. This paper presents the first polynomial time, approximation algorithm for the Min Assignment problem. The algorithm guarantees an approximation ratio of 2 and runs in time O(hn3). We also prove that, for constant h and for "well spread" instances (a broad generalization of the uniform chain case), we can find a solution in time O(hn3) whose cost is at most an (1 + Ɛ(n)) factor from the optimum, where Ɛ(n) = o(1) and n is the number of stations. This result significantly improves the approximability result by Kirousis et al on uniform chains. Both of our approximation results are obtained by new algorithms that exactly solves two natural variants of the Min Assignment problem that might have independent interest: the All-To-One problem (in which every station must reach a fixed one in at most h hops) and the Base Location problem (in which the goal is to select a set of Basis among the stations and all the other stations must reach one of them in at most h -1 hops). Finally, we show that for h = 2 the Min Assignment problem can be solved in O(n3)-time.