The minimum range assignment problem on linear radio networks (Extended abstract)
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN: 1611-3349, Vol: 1879, Page: 143-154
2000
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Book Chapter Description
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(hn). 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(hn) whose cost is at most an (1 + (n)) factor from the optimum, where (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(n)-time.
Bibliographic Details
Springer Science and Business Media LLC
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