On percolation connectivity of large scale wireless networks with directional antennas

We investigate the percolation connectivity of wireless ad hoc networks with directional antennas (called DIR networks). One of major concerns is to derive bounds on the number of edge-disjoint directed paths (or highways). However, it is non-trivial to obtain bounds on the number of directed highways in DIR networks since the conventional undirected percolation theory cannot be directly used in DIR networks. In this paper, we exploit the directed percolation theory to derive bounds on the number of directed highways. In particular, we make new constructions in bond directed percolation model. We show that with high probability there are at least Ω(√n/log log √n) directed highways in a network with n nodes, which is much tighter than the existing results in DIR networks.