Distributed Homology-based Algorithm for solving Set k-Cover problem in Heterogeneous Directional Sensor Networks

Coverage is one of the fundamental problems in directional sensor networks (DSNs). This problem is more complicated when we deal with heterogeneous DSNs (HDSNs). Prolonging the network lifetime is another important problem in this area. The problem of finding k disjoint cover sets known as the Set k-Cover problem can solve both the coverage and lifetime issues. In this paper a distributed algorithm is proposed for the Set k-Cover problem in HDSNs and then the method is applied for target k-tracking problem. In the Set k-Cover problem, directional sensors are partitioned into k disjoint sets where each set covers the entire area, and in object k -tracking problem, the object must be tracked by at least k sensors. The proposed algorithms are based on the notion of homology in Algebraic Topology. We consider the Nerve complex corresponding to the HDSN and demonstrate how topological properties of the Nerve complex of the network can be used to formulate the Set k-Cover problem as an integer linear programming problem. Then, we propose a distributed algorithm based on the subgradient method for this problem. After that, we propose a distributed algorithm for object k-tracking based on the solution of the Set k-Cover problem. Finally, we evaluate the performance of the proposed algorithms by conducting simulation experiments.