Network virtualization provides a promising solution to overcome the ossification of current networks, allowing multiple Virtual Network Requests (VNRs) to be embedded on a common infrastructure. The major challenge in network virtualization is the Virtual Network Embedding (VNE) problem, which is to embed VNRs onto a shared substrate network and known to be $\mathcal {NP}$ -hard. The topological heterogeneity of VNRs is one important factor hampering the performance of the VNE. However, in many specialized applications and infrastructures, VNRs are of some common structural features, e.g., paths and cycles. To achieve better outcomes, it is thus critical to design dedicated algorithms for these applications and infrastructures by taking into accounting topological characteristics. Besides, paths and cycles are two of the most fundamental topologies that all network structures consist of. Exploiting the characteristics of path and cycle embeddings is vital to tackle the general VNE problem. In this paper, we investigate the path and cycle embedding problems. For path embedding, we prove its $\mathcal {NP}$ -hardness and inapproximability. Then, by utilizing Multiple Knapsack Problem (MKP) and Multi-Dimensional Knapsack Problem (MDKP), we propose an efficient and effective MKP-MDKP-based algorithm. For cycle embedding, we propose a Weighted Directed Auxiliary Graph (WDAG) to develop a polynomial-time algorithm to determine the least-resource-consuming embedding. Numerical results show our customized algorithms can boost the acceptance ratio and revenue compared to generic embedding algorithms in the literature.

中文翻译：

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关于虚拟网络嵌入：路径和循环

网络虚拟化提供了一种有前途的解决方案来克服当前网络的僵化，允许将多个虚拟网络请求 (VNR) 嵌入到公共基础设施中。网络虚拟化的主要挑战是虚拟网络嵌入 (VNE) 问题，即将 VNR 嵌入到共享的底层网络中，并且已知为 $\mathcal {NP}$ -hard。VNR 的拓扑异质性是阻碍 VNE 性能的重要因素之一。然而，在许多专门的应用程序和基础设施中，VNR 具有一些常见的结构特征，例如路径和循环。因此，为了获得更好的结果，通过考虑拓扑特征为这些应用程序和基础设施设计专用算法至关重要。除了，路径和循环是所有网络结构都包含的两种最基本的拓扑结构。利用路径和循环嵌入的特征对于解决一般的 VNE 问题至关重要。在本文中，我们研究了路径和循环嵌入问题。对于路径嵌入，我们证明了它的 $\mathcal {NP}$ -hardness 和不可近似性。然后，通过利用多背包问题（MKP）和多维背包问题（MDKP），我们提出了一种高效且有效的基于 MKP-MDKP 的算法。对于循环嵌入，我们提出了加权有向辅助图 (WDAG) 来开发多项式时间算法来确定最少资源消耗的嵌入。数值结果表明，与文献中的通用嵌入算法相比，我们的定制算法可以提高接受率和收入。