Sensor network connectivity with multiple directional antennae of a given angular sum

We investigate the problem of converting sets of sensors into strongly connected networks of sensors using multiple directional antennae. Consider a set S of n points in the plane modeling sensors of an ad hoc network. Each sensor uses a fixed number, say 1 ≤ k ≤ 5, of directional antennae modeled as a circular sector with a given spread (or angle) and range (or radius). We give algorithms for orienting the antennae at each sensor so that the resulting directed graph induced by the directed antennae on the nodes is strongly connected. We also study trade-offs between the total angle spread and range for maintaining connectivity.