Minimum energy broadcast on rectangular grid wireless networks

The minimum energy broadcast problem is to assign a transmission range to each node in an ad hoc wireless network to construct a spanning tree rooted at a given source node such that any non-root node resides within the transmission range of its parent. The objective is to minimize the total energy consumption, i.e., the sum of the δth powers of a transmission range (δ<1). In this paper, we consider the case that δ=2, and that nodes are located on a 2-dimensional rectangular grid. We prove that the minimum energy consumption for an n-node k×l-grid with n=kl and k≤l is at most nπ+O(n k0.68) and at least nπ+Ω(nk)-O(k). Our bounds close the previously known gap of upper and lower bounds for square grids. Moreover, our lower bound is n3-O(1) for 3≤k≤18, which matches a naive upper bound within a constant term for k≡0(mod3). © 2011 Elsevier B.V. All rights reserved

Tightening the upper bound for the Minimum Energy Broadcasting

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