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By integrating software defined network and network function virtualization, software defined satellite networks (SDSNs) can enable flexible virtual network function (VNF) deployment to process and forward end-to-end traffic flows. Since one traffic flow has to go through all its required VNFs, the VNF deployment has a significant impact on traffic routing. In this regard, with time-varying network topology and limited network resources taken into account, we aim to match VNF deployment and routing to fulfill traffic flows' requirements in the SDSN in a cost-effective manner. Specifically, we first evolve the traditional time evolving graph as a software defined time evolving graph (SDTEG) to depict the time-varying network topology and meanwhile, provide a shared platform for elastic network resource provisioning. On this basis, we then formulate a cost minimization problem as a multi-slot integer linear programming …