Maximizing the Number of Broadcast Operations in Static Random Geometric Ad-Hoc Networks

Abstract

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 Max LifeTime, is known to be NP-hard and the best algorithm yields worst-case approximation ratio Θ(log n), 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 √ 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.

Minimum-energy broadcast in random-grid ad-hoc networks

“…At every new operation, the pivot task is indeed assigned to nodes according to a Round Robin rule. We show this yields an almost optimal life-time of the network according to the energy consumption model in [5,7]. As for the single broadcast scenario, the completion time of our protocol is slower than the optimum by a Θ(log n) factor.…”

“…This assumption is reasonable in static ad-hoc networks since every node can store once and for ever its position in the set-up phase. The protocol exploits a fully-distributed pivot-election strategy borrowed from [5]. We prove that the work complexity of the protocol is equivalent to the energy cost of the centralized version and hence, thanks again to our lower bound (clearly, a lower bound for the energy cost is also a lower bound for the work complexity), it achieves a constant approximation ratio as well.…”

“…Moreover, for every a, c > 0, it holds that a log c a ≤ c e log e. Thus, by setting a = δp min ǫ 5 and c = (64eπ) 1 6 , we get…”

“…In such a case, we aim to design solutions that are well energy-load balanced. Notice that, in the many-broadcast scenario, this corresponds to maximize network lifetime according to the model in [6,7].…”

“…Our protocol yields a good energy-load balanced solution: there are Θ(n/ log n) pivots, i.e., the nodes having range Θ( √ log n) (the remaining nodes have range 0). Furthermore, thanks to the pivot-election strategy [6], a good energyload balance is also obtained with respect to an arbitrary sequence of broadcast operations, i.e., for the many-broadcast scenario. At every new operation, the pivot task is indeed assigned to nodes according to a Round Robin rule.…”