Broadcast is a fundamental network operation, widely used in wireless networks to disseminate messages. The energy-efficiency of broadcast is important particularly when devices in the network are energy constrained. To improve the efficiency of broadcast, different approaches have been taken in the literature. One of these approaches is broadcast with energy accumulation. Through simulations, it has been shown in the literature that broadcast with energy accumulation can result in energy saving. The amount of this saving, however, has only been analyzed for linear multi-hop wireless networks. In this work, we extend this analysis to two-dimensional (2D) multi-hop networks. The analysis of saving in 2D networks is much more challenging than that in linear networks. It is because, unlike in linear networks, in 2D networks, finding minimum-energy broadcasts with or without energy accumulation are both NP-hard problems. Nevertheless, using a novel approach, we prove that this saving is constant when the path loss exponent alpha is strictly greater than two. Also, we prove that the saving is theta(log n) when alpha=2, where n denotes the number of nodes in the network.
The best existing approximation algorithm to the problem is, however, due to Caragiannis, Flammini, and Moscardelli @cite_25 . In 2D wireless networks, their algorithm has an approximation ratio of 4.2 for Euclidean cost graphs, and a logarithmic approximation for non-Euclidean cost graphs.
@cite_25
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We present a new approximation algorithm for the Minimum Energy Broadcast Routing (MEBR) problem in ad hoc wireless networks that achieves an exponentially better approximation factor compared to the well-known Minimum Spanning Tree (MST) heuristic. Namely, for any instance where a minimum spanning tree of the set of stations is guaranteed to cost at most ρ ≥ 2 times the cost of an optimal solution for MEBR, we prove that our algorithm achieves an approximation ratio bounded by 2 ln ρ - 2 ln 2 +2. This result is particularly relevant for its consequences on Euclidean instances where we significantly improve previous results. In this respect, our experimental analysis confirms the better performance of the algorithm also in practice.