For the connectivity of wireless ad hoc network, we have the following results:
1. In 1D, we used the following techniques to obtain the results (from less accurate to exact result).
a) Isolated node: Analyse the probability of the existence of an isolated node.
b) Occupancy theory: subdivide the interval into "cells" of length r (the transmission range). If there exists an empty cell separating two cells that each contains at least one node, then the network is disconnected.
c) Random Interval Graph: The existence of the big spacings. (exact result)
2. In 2D, we do not have the exact result. Instead, the following techniques are used to obtain the asymptotic results.
a) Isolated node: The existence of an isolated node
From 1D results, we can predict that using occupancy theory may improve the results obtained under 2D networks. From observing the occupancy theory methodology, I assume there are two directions that we can look into the connectivity problem.
a) Divide the 2D area into cells and start from here.
b) Look at nodes lying within a certain sector of angle but are not directly connected.
I could not tell any further until I have more concrete ideas on that.