Distributed Construction of a Planar Spanner and Routing for Ad Hoc Wireless Networks

Several localized routing protocols [1] guarantee the delivery of the packets when the underlying network topology is the Delaunay triangulation of all wireless nodes. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we more accurately model the network as a unit-disk graph UDG , in which a link in between two nodes exist only if the distance in between them is at most the maximum transmission range. Given a graph H , a spanning subgraph G of H is a t-spanner if the length of the shortest path connecting any two points in G is no more than t times the length of the shortest path connecting the two points in H . In this paper, we present a novel localized networking protocol that constructs a planar 2:5-spanner of UDG , called the localized Delaunay triangulation, as network topology. It contains all edges that are both in the unit-disk graph and the Delaunay triangulation of all wireless nodes. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. The total communication cost of our networking protocol is O(n log n) bits. Moreover, the computation cost of each node u is O(du log du), where du is the number of 1-hop neighbors of u in UDG .