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Space-Ground Integrated Network (SGIN) is a multi-domain integrated network with a large coverage area, which can better meet the ubiquitous communication needs in the network and provide users with better services. It has become the main development direction of 6G network. The different networks integrated in SGIN are heterogeneous, which is specifically reflected in the fact that the periodic movement of satellite networks brings time-varying nature to resources, and the expansion of network scale also brings spatial attributes to resources. It can be concluded that resources in SGIN have multi-dimensional. When performing virtual network embedding(VNE) in SGIN, the existing embedding algorithms often do not consider the multi-dimensionality of resources, which may lead to problems such as spatially dispersed embedding results and inability to adapt to network dynamic changes. To address this problem, this paper uses the space-time resource tree(S-TRT) model to represent the multi-dimensional resources in SGIN, reflecting the performance of resources in four dimensions: time, space, type, and quantity. On the basis of this model, combined with multiple dimensions of resources and the spatial distribution of embedded nodes, the ranking vector of virtual nodes is established, and the dimensionality reduction sorting of each virtual node is carried out by multi-dimensional scaling method. Afterwards, the node embedding is completed by dynamically sorting the physical nodes to improve the spatial concentration of the embedding results and better adapt to the dynamic changes of the underlying network. Finally, we conducted a simulation experiment on the algorithm, and the results show that the algorithm has good performance in the request acceptance rate and long-term revenue-to-cost ratio.
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