Directional versus omnidirectional antennas for energy consumption and k -connectivity of networks of sensors

A network is k-connected if it remains connected after the removal of any k–1 of its nodes. Assume that n sensors, modeled here as (omni)directional antennas, are dropped randomly and independently with the uniform distribution on the interior of a unit length segment or a unit square. We derive sufficient conditions on the beam width of directional antennas so that the energy consumption required to maintain k-connectivity of the resulting network of sensors is lower when using directional than when using omnidirectional antennas. Our theoretical bounds are shown by experiment to be accurate under most circumstances. For the case of directional antennae, we provide simple algorithms for setting up a k-connected network requiring low energy.