Network Function Virtualization (NFV) is a promising paradigm which can increase network flexibility by deploying newly network services into networks. Because of the flexibility, NFV is also considered as one of the building blocks for 5G and edge computing. However, the intrinsic dynamic features of NFV and the rigorous requirements proposed by 5G and edge computing, such as delay, pose significant challenges to make the optimal Virtual Network Function (VNF) chain placement. To address this problem, we first formulate the VNF chain placement problem as an integer linear programming problem with taking the dynamic characteristics in to consideration. Then we propose an efficient dynamic algorithm, called DynAmic vnF placemenT (DAFT), which provides a good solution for VNF chain placement. DAFT is based on primal–dual technique and combines with an efficient subroutine which is solved by reducing to the shortest path problem. The theoretic analysis shows DAFT is $(1-1∕e)$-competitive to offline optimal solution. We also propose a modified algorithm concerning algorithm implementation issues, which is called Feasible DAFT (FDAFT). Finally, we evaluate the proposed algorithms through extensive numerical simulations. The experiment results show that DAFT and FDAFT achieve average competitive ratios up to 98.42% and 96.74%, respectively and outperform the compared algorithms around 50%.

网络功能虚拟化（NFV）是一种有前途的范例，可以通过将新的网络服务部署到网络中来增加网络灵活性。由于灵活性，NFV也被视为5G和边缘计算的组成部分之一。但是，NFV的固有动态特性以及5G和边缘计算提出的严格要求（例如延迟）对做出最佳虚拟网络功能（VNF）链放置提出了重大挑战。为了解决这个问题，我们首先考虑到动态特性，将VNF链放置问题公式化为整数线性规划问题。然后，我们提出了一种有效的动态算法，称为DynAmic vnF placemenT（DAFT），它为VNF链放置提供了一个很好的解决方案。DAFT基于原始对偶技术，并结合了有效的子例程，该子例程可通过简化为最短路径问题来解决。理论分析表明DAFT为$（\mathrm{1个}-\mathrm{1个}∕Ë）$-与离线最佳解决方案竞争。我们还提出了一种与算法实现问题有关的改进算法，称为可行DAFT（FDAFT）。最后，我们通过广泛的数值模拟评估提出的算法。实验结果表明，DAFT和FDAFT的平均竞争率分别达到98.42％和96.74％，并且比比较算法高出约50％。