Tight Bounds on Localized Sensor Self-Deployment for Focused Coverage

We consider the self-deployment problem in mobile sensor networks with the objective of providing focused coverage for a point of interest (POI) such that the maximum area around it is covered by sensors without sensing holes. We present a local greedy algorithm, called TTGREEDY, that solves this problem in at most R + 2.(n-1) time steps, where R is the distance to the farthest initial sensor position from the POI and n is the number of sensors. This is a significant improvement over the best previously known O(D) time step algorithm of Blazovics and Lukovszki, where D is the sum of the initial distances to the sensors from the POI. The main idea is to synchronously drive mobile sensors along a locally-computed triangle tessellation avoiding collisions of sensors. We also show that there are initial configurations of n sensors in this problem where at least R + (n-1)/2 time steps are needed by any greedy algorithm. These results provide the first tight runtime (within a small constant factor) solution to this problem.