An Edge Constrained Localized Delaunay Graph for Geographic Routing in Mobile Ad Hoc Networks

In this paper, we propose an edge constrained localized Delaunay graph, ECLDel, as the underlying graph for geographic routing in mobile ad hoc networks. We prove that the ECLDel is a planar t-spanner of the original unit-disk graph. We give an algorithm to construct the ECLDel, which can be run by each node distributively with 1-hop neighborhood information. We define two new kinds of edges, the intersecting Gabriel (IG) edges and the unaware intersection (UI) edges, which are constrained in the ECLDel. This makes the construction of ECLDel more efficient and converges faster with less communication cost, compared to the previous work of constructing a planarized localized Delaunay graph, PLDel. The simulation results show that the average number of messages and the average size of messages (the number of neighbor nodes in the messages) broadcast by each node in construction of ECLDel is 65% and 42% less than that in construction of PLDel, respectively.