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In this paper, we propose a novel Space-Air-Ground Integrated Networks (SAGINs) architecture based on cloud-edge collaboration leveraging network function virtualization (NFV). The cloud-based services are provisioned by the selected ground datacenters (DCs) and the traffic is processed by the virtual network function (VNF) hosted in edge nodes and DCs. DCs provide various cloud-oriented network services, and edge nodes enable flexible solutions for SFC provisioning. We apply anycast to further improve the agility of SFC provisioning. From these perspectives, we investigate the cloud-serving and edge-processing SFC provisioning problem leveraging anycast, concerning DC assignment, edge and VNF placement, and SFC mapping simultaneously. A mixed integer linear program (MILP) model is formulated to jointly minimize the communication and computation cost subject to their trade-off. A …