Constructing minimum energy mobile wireless networks

Abstract

Energy conservation is a critical issue in designing wireless ad hoc networks, as the nodes are powered by batteries only. Given a set of wireless network nodes, the directed weighted transmission graph G t has an edge uv if and only if node v is in the transmission range of node u and the weight of uv is typically defined as || uv || α + c for a constant 2 ≤ α ≤ 5 and c > 0 . The minimum power topology G m is the smallest subgraph of G t that contains the shortest paths between all pairs of nodes, i.e., the union of all shortest paths. In this paper, we described a distributed position-based networking protocol to construct an enclosure graph G e , which is an approximation of G m . The time complexity of each node u is O (min( d G t (u) d G e (u), d G t (u) log d G t (u))), where d G (u) is the degree of node u in a graph G. The space required at each node to compute the minimum power topology is O ( d G t (u)). This improves the previous result that computes G m in O ( d G t (u) 3 ) time using O ( d G t (u) 2 ) spaces. We also show that the average degree d G e (u) is usually a constant, which is at most 6. Our result is first developed for stationary network and then extended to mobile networks.