Distributed Construction of 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 often model the network as a unit-disk graphUDG . In this paper, we present a novel localized networking protocol that constructs a planar spanner, 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 routing protocols are increased when localized Delaunay triangulation is used instead of some other previous known planar topologies. In addition, we prove that the shortest path connecting any pair of wireless nodes has length no more than a small (< 2:5) constant factor of the length of the shortest path in UDG . The total communication cost of our algorithm 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 .