Network slicing is a critical feature in 5G and beyond communication systems, enabling the creation of multiple virtual networks (i.e., slices) on a shared physical network infrastructure. This involves efficiently mapping each slice component, including virtual network functions (VNFs) and their interconnections (virtual links), onto the physical network. This paper considers slice embedding problem in which the order of VNFs can be adjusted, providing increased flexibility for service deployment on the infrastructure. This also complicates embedding, as the best order has to be selected. We propose an innovative optimization framework to tackle the challenges of jointly optimizing slice admission control and embedding with flexible VNF ordering. Additionally, we introduce a near-optimal branch-and-bound (BnB) algorithm, combined with the A* search algorithm, to generate embedding solutions efficiently. Extensive simulations on both small and large-scale scenarios demonstrate that flexible VNF ordering significantly increases the number of deployable slices within the network infrastructure, thereby improving resource utilization and meeting diverse demands across varied network topologies.

翻译：网络切片是5G及未来通信系统中的关键特性，能够在共享的物理网络基础设施上创建多个虚拟网络（即切片）。这涉及将每个切片组件（包括虚拟网络功能及其互连的虚拟链路）高效映射到物理网络。本文研究切片嵌入问题，其中虚拟网络功能的顺序可以调整，从而为基础设施上的服务部署提供更大的灵活性。这也使得嵌入过程复杂化，因为必须选择最优顺序。我们提出了一种创新的优化框架，以应对联合优化切片准入控制和具有灵活虚拟网络功能排序的嵌入问题所带来的挑战。此外，我们引入了一种结合A*搜索算法的近似最优分支定界算法，以高效生成嵌入解决方案。在小型和大型场景下的大量仿真实验表明，灵活的虚拟网络功能排序能显著增加网络基础设施内可部署的切片数量，从而提高资源利用率并满足不同网络拓扑下的多样化需求。