Aerial Platform Placement Algorithm to Satisfy Connectivity and Capacity Constraints in Wireless Ad-Hoc Networks

In this paper, we address the problem of establishing full connectivity and satisfying required traffic capacity between disconnected clusters in large wireless ad-hoc ground networks by placing a minimum number of advantaged high flying aerial platforms (APs) as relay nodes at appropriate places. We formulate the problem of providing both connectivity and required capacity between disconnected ground clusters as a constrained clustering problem with complexity costs. The basic requirement for connectivity between the ground clusters and APs is converted into a summation form distortion function. The additional requirement for connectivity between the various APs is encoded by adding a new (summation form) constraint to the distortion function. In order to satisfy the required capacity out of each cluster to all other clusters, we add a cost function that depends on the assignment probabilities of the APs and relate the source (prior) probabilities of each cluster to the required capacity out of this cluster. The cost function produces solutions which are load balanced, i.e., the capacities supported through each AP are nearly equal. We solve the resultant clustering problem using deterministic annealing in order to find (near) globally optimal solutions for the minimum number and locations of the APs to establish full connectivity and provide required traffic capacity between disconnected clusters. We establish the validity of our algorithm by comparing it with optimal exhaustive search algorithms and show that our algorithm is near-optimal for the problem of establishing connectivity and satisfying capacity requirements between disconnected clusters.