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 n/π + O (n/k0.68) and at least n/π + Δ (n/k) - O(k).Our bounds close the previously known gap of upper and lower bounds for square grids. Moreover, our lower bound is n/3 - O(1) for 3 ≤ k ≤ 18, which matches a naive upper bound within a constant term for k ≡ 0 (mod 3). © 2010 Springer-Verlag.
CITATION STYLE
Murata, A., & Matsubayashi, A. (2010). Minimum energy broadcast on rectangular grid wireless networks. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6451 LNCS, pp. 34–46). Springer Verlag. https://doi.org/10.1007/978-3-642-16988-5_4
Mendeley helps you to discover research relevant for your work.