Issue No. 02 - February (2011 vol. 22)

ISSN: 1045-9219

pp: 208-216

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TPDS.2010.77

Tiziana Calamoneri , Sapienza Università di Roma, Roma

Andrea E.F. Clementi , Università degli studi di Roma Tor Vergata, Roma

Emanuele G. Fusco , Sapienza Università di Roma, Roma

Riccardo Silvestri , Sapienza Università di Roma, Roma

ABSTRACT

We consider static ad hoc wireless networks whose nodes, equipped with the same initial battery charge, may dynamically change their transmission range. When a node v transmits with range r(v), its battery charge is decreased by \beta r(v)^2, where \beta >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 by the length of the schedule). This maximization problem, denoted by Max LifeTime, is known to be NP-hard and the best algorithm yields worst-case approximation ratio \Theta (\log n), where n is the number of nodes of the network. 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 present an efficient algorithm that constructs a range assignment schedule having length not smaller than 1/12 of the optimum with high probability. Then we 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.

INDEX TERMS

Energy-aware systems, wireless communication, graph algorithms, network problems.

CITATION

Tiziana Calamoneri, Andrea E.F. Clementi, Emanuele G. Fusco, Riccardo Silvestri, "Maximizing the Number of Broadcast Operations in Random Geometric Ad Hoc Wireless Networks",

*IEEE Transactions on Parallel & Distributed Systems*, vol. 22, no. , pp. 208-216, February 2011, doi:10.1109/TPDS.2010.77SEARCH