Localised alpha-shape computations for boundary recognition in sensor networks

Intuitively, many wireless and sensing applications benefit from knowledge of network boundaries. Many virtual coordinate constructions rely on the furthest set of nodes as beacons. Network edges may also bound routing holes in the network, regions of failure due to environmental effects, or indicate the need for additional deployment. In this paper we solve the edge detection problem locally using a geometric structure called the alpha-shape (@a-shape). For a disc of radius 1/@a, the @a-shape consists of nodes (and joining edges) that sit on the boundary of the discs that contain no other nodes in the network. In the simplest terms a node decides it is on a network boundary by asking the following question: ''Do I sit on the boundary of a disc of radius 1/@a that contains no other nodes in the network?'' We show that using only local communications our algorithm is provably correct. Boundary nodes may further participate to reduce unwanted detail. We show via simulation that our algorithm identifies meaningful boundaries even in networks of low-density and non-uniform distribution.