Abstract
We consider static ad-hoc wireless networks where nodes have the same initial battery charge and they may dynamically change their transmission range at every time slot. When a node v transmits with range r(v), its battery charge is decreased by β×r(v)2 where β> 0 is a fixed constant.
The goal is to provide a range assignment schedule that maximizes the number of broadcast operations from a given source (this number is denoted as the length of the schedule). This maximization problem, denoted as 
, is known to be 
-hard and the best algorithm yields worst-case approximation ratio Θ(logn), where n is the number of nodes of the network [5].
We consider random geometric instances formed by selecting n points independently and uniformly at random from a square of side length \(\sqrt{n}\) in the Euclidean plane.
We first present an efficient algorithm that constructs a range assignment schedule having length, with high probability, not smaller than 1/12 of the optimum.
We then design an efficient distributed version of the above algorithm where nodes initially know n and their own position only. The resulting schedule guarantees the same approximation ratio achieved by the centralized version thus obtaining the first distributed algorithm having provably-good performance for this problem.
Research partially supported by the European Union under the Project IP-FP6-015964 AEOLUS.
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Calamoneri, T., Clementi, A., Fusco, E.G., Silvestri, R. (2007). Maximizing the Number of Broadcast Operations in Static Random Geometric Ad-Hoc Networks. In: Tovar, E., Tsigas, P., Fouchal, H. (eds) Principles of Distributed Systems. OPODIS 2007. Lecture Notes in Computer Science, vol 4878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77096-1_18
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DOI: https://doi.org/10.1007/978-3-540-77096-1_18
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