Minimum Energy Broadcast on Rectangular Grid Wireless Networks

Abstract

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