Connectivity with directional antennas in the symmetric communication model.

We study the problem of connectivity in wireless networks in which each node uses a single directional antenna. We consider the symmetric model of communication with directional antennas. In this model, two nodes are connected by a link if and only if they lie in the transmission sectors of each other's antenna. Given nodes located in the plane, each with an antenna of beamwidth ϕ and radius r, we study the problem of orienting the antennas in such a way as to create a connected network. We show that for ϕ<π/3 and a given radius, the problem of determining the existence of an orientation that ensures a connected network is NP-complete. For ϕ≥π/2, in which case connectivity is known to be always possible, we study the problem of achieving connectivity while minimizing the radius. For different ranges of ϕ, we give approximation algorithms that achieve connectivity while using a radius that is at most a constant times the optimal radius. Some of our algorithms also have provable bounds on the stretch factor of the resulting network compared to a network of nodes with omnidirectional antennas of a given radius.