Distributed cloud networking builds on network functions virtualization (NFV) and software defined networking (SDN) to enable the deployment of network services in the form of elastic virtual network functions (VNFs) instantiated over general purpose servers at distributed cloud locations. We address the design of fast approximation algorithms for the NFV service distribution problem (NSDP), whose goal is to determine the placement of VNFs, the routing of service flows, and the associated allocation of cloud and network resources that satisfy client demands with minimum cost. We show that in the case of load-proportional costs, the resulting fractional NSDP can be formulated as a multi-commodity-chain flow problem on a cloud augmented graph, and design a queue-length based algorithm, named QNSD, that provides an O(\epsilon) approximation in time O(1/\epsilon). We then address the case in which resource costs are a function of the integer number of allocated resources and design a variation of QNSD that effectively pushes for flow consolidation into a limited number of active resources to minimize overall cloud network cost.

翻译：分布式云层网络建立在网络功能虚拟化(NFV)和定义的网络化软件(SDN)的基础上,从而能够在分布式云点的通用服务器上即刻部署以弹性虚拟网络功能(VNFs)为形式的网络服务。我们处理NFV服务分布问题快速近似算法的设计问题,其目标是确定VNF服务分布问题的定位、服务流动的路线以及相关的云和网络资源的分配,从而以最低成本满足客户的需求。我们表明,在负载比例成本的情况下,由此产生的零散NSDP可以形成成一个云增大图上的多通货链流问题,并设计一个以队列为基础的算法,名为QNSD,提供O(1/\epsilon)时间的O(1/\epsilon)近似值。然后我们处理资源成本是分配资源整数的函数,并设计QNSD的变换,从而有效地推动流动整合成数量有限的主动网络成本。