Heterogeneous Sensor Network Deployment Using Circle Packings

This paper addresses the problem of deploying a set of mobile sensor nodes of heterogeneous sensing ranges to give a large and connected coverage. A novel deployment algorithm based on the circle packing technique is given. It iteratively enhances the coverage area of the sensor network from an initial random deployment, while guarantees the absence of coverage hole and obstacle avoidance. The sensing area of each node is modeled as a circular disc while its radius is bounded by the corresponding sensing range limit. The problem of placing these circular discs to cover a field is intuitively transformed to the circle packing problem: given the specified combinatorics of tangency patterns of n circles, find the label R denoting the radii of these circles. Since a unique packing exists for any given set of triangulations and boundary conditions, we can always find the minimum sensing range required for every interior node to satisfy such packing conditions. Though an extension from tangency packing to overlap packing, the interstices among triples (which represent coverage holes) can be eliminated. We have proven that the maximum global scaling factor to vanish all possible interstices is alpha = 3^((1/2)/2. Based on a number of numerical simulations, we have verified that the proposed algorithm always yields sensor deployments of wide coverage and minimize the sensing ranges required for every interior sensing node to satisfy the packing and boundary conditions.