Weighted Algebraic Connectivity Maximization for Optical Satellite Networks

• Published in: IEEE access Vol. 5; pp. 6885 - 6893
• Main Authors: Zheng, Yongxing, Zhao, Shanghong, Liu, Yun, Li, Yongjun, Tan, Qinggui, Xin, Ning
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive optics; Algebra; Algorithms; Computational geometry; Convex functions; convex optimization; Convexity; greedy heuristic; Heuristic methods; matrix perturbation; Network topology; Optical communication; Optical fiber networks; Optical satellite networks; Optimization; Perturbation theory; Polynomials; Reconfiguration; Satellite networks; Satellites; Semidefinite programming; Topology; weighted algebraic connectivity
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2017.2697818

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.