## 2 Related Work
### Virtual Network Mapping  
The process of virtual network mapping involves the mapping of virtual network requests (VNR) to physical network resources. Through the design of suitable virtual network mapping algorithms, it becomes feasible to optimize the utilization of physical network resources, enhance resource efficiency, and diminish the cost associated with virtual network mapping. In the early stages of research on virtual network mapping problems, many researchers have proposed many heuristic algorithms. [PERSON] et al. [15; 16] proposed an efficient mapping algorithm that utilized a novel node-ranking method for embedding virtual networks. Building upon this work, the researchers further developed an embedding algorithm based on multiple topological attributes, which not only considered the importance of individual nodes, but also incorporated the overall network topology. This approach aimed to achieve more efficient resource allocation and improve overall network performance. [PERSON] et al. [17] proposed a security-aware virtual network embedding algorithm that leveraged information entropy and the TOPSIS method to optimize network security. The algorithm took into account resource allocation efficiency to ensure that security enhancements were achieved without significantly compromising resource efficiency. Similarly, [PERSON] et al. [18] introduced a collaborative dynamic virtual network embedding algorithm based on a resource importance metric. By dynamically evaluating the importance of resources, this algorithm aimed to achieve efficient resource utilization under constrained resource conditions. However, these heuristic algorithms on resource allocation and resource efficiency are either constrained by the scale of the network or limited to single-domain networks. As the scale of virtual networks continues to expand, it may become very time-consuming or impossible to find effective solutions. [PERSON] et al. [19] introduced reinforcement learning to optimize node mapping, which improved the request acceptance rate and long-term benefits compared to traditional heuristic algorithms, proving the effectiveness of reinforcement learning in virtual network mapping problems. [PERSON] et al. [20] introduced a virtual network embedding algorithm grounded in enhanced genetic algorithms, yielding a substantial enhancement in the acceptance rate of VNR and the long-term average revenue of Infrastructure Providers (InPs). [PERSON] et al. [21] asserted that prior VNE algorithms overlooked the resource situation of the underlying network (RSUN). Consequently, they devised two heuristic algorithms designed to choose suitable VNE strategies based on RSUN. Through the categorization of physical nodes, the efficacy of bandwidth utilization witnessed significant improvement. [PERSON] et al. [22] introduced a VNE algorithm founded on Q-learning algorithm, which improved resource utilization compared to traditional heuristic algorithms. Since most algorithms did not consider the QoS requirements of VNR, and a few only considered the mapping of delay-sensitive VNR [23; 24; 25], [PERSON] et al. [26] proposed a VNE algorithm rooted in deep reinforcement learning (DRL), which focused on differentiated service quality requirements and network security issues. [PERSON] et al. [27] believed that most VNE methods only focus on the current VNR and treat different QoS requirements equally, ignoring long-term effects. Therefore, they proposed a hierarchical reinforcement-learning-based active virtual network embedding algorithm (VNE-HRL). [PERSON] et al. [28] introduced a pair of distributed parallel genetic algorithms employing crossover and mutation schemes for addressing online virtual network link embedding challenges. Two algorithms collaborated with each other and demonstrated a speed improvement of 32.78% compared to the prevalent VNE algorithms of the era.