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Abstract: The Min Energy broadcast problem consists in assigning transmission ranges tothe nodes of an ad-hoc network in order to guarantee a directed spanning treefrom a given source node and, at the same time, to minimize the energyconsumption i.e. the energy cost yielded by the range assignment. Min energybroadcast is known to be NP-hard.We consider random-grid networks where nodes are chosen independently atrandom from the $n$ points of a $\sqrt n \times \sqrt n$ square grid in theplane. The probability of the existence of a node at a given point of the griddoes depend on that point, that is, the probability distribution can benon-uniform.By using information-theoretic arguments, we prove a lower bound$1-\epsilon \frac n{\pi}$ on the energy cost of any feasible solution forthis problem. Then, we provide an efficient solution of energy cost not largerthan $1.1204 \frac n{\pi}$.Finally, we present a fully-distributed protocol that constructs a broadcastrange assignment of energy cost not larger than $8n$,thus still yieldingconstant approximation. The energy load is well balanced and, at the same time,the work complexity i.e. the energy due to all message transmissions of theprotocol is asymptotically optimal. The completion time of the protocol isonly an $O\log n$ factor slower than the optimum. The approximation qualityof our distributed solution is also experimentally evaluated.All bounds hold with probability at least $1-1-n^{\Theta1}$.



Autor: Tiziana Calamoneri, Andrea E.F. Clementi, Angelo Monti, Gianluca Rossi, Riccardo Silvestri

Fuente: https://arxiv.org/







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