Fast transmission in ad hoc networks

In this paper, various fast transmission strategies for sending information from a source s over a large distance to a target t in ad hoc wireless networks where the nodes are distributed as a Poisson process of intensity is presented. The existence of an infinite component, i.e., percolation, is not sufficient for our problem since the proportion of vertices in the infinite component may be very low. To achieve connectivity the power must increase with the number of vertices, since there is some positive chance that a vertex is isolated. Result shows that with directional transmissions, even with very low power there exist points at arbitrarily large distance that can communicate.