Weighted Algebraic Connectivity Maximization for Optical Satellite Networks

In this paper, the topology configuration methods for heterogeneous optical satellite networks are investigated. Our objectives are to maximize weighted algebraic connectivity with respect to both network initialization and reconfiguration scenarios subject to onboard hardware constraints. The problems are not strictly convex and have been proven as NP-hard. In order to solve the problems in polynomial time, the original problems are relaxed to a convex optimization problem. Specifically, the relaxed problem is transformed to a positive semidefinite programming form, which can be solved exactly and more efficiently. Furthermore, based on the perturbation theory of matrices, we propose two greedy heuristic methods to deal with the initialization and reconfiguration case from the relaxed solutions, respectively. Simulation results show that the proposed algorithms are able to accomplish network initialization and reconfiguration correctly in the overwhelming majority of situations. The final sub-optimal solutions can also be obtained under low computational complexity.