@article{oai:kanazawa-u.repo.nii.ac.jp:00008371,
 author = {Murata, Atsushi and Matsubayashi, Akira},
 issue = {39},
 journal = {Theoretical Computer Science},
 month = {Sep},
 note = {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.},
 pages = {5167--5175},
 title = {Minimum energy broadcast on rectangular grid wireless networks},
 volume = {412},
 year = {2011}
}