This paper proposes a set of algorithms to extend initially deployed Virtualized Network Functions Forwarding Graphs (VNF-FG or Service Function Chains - SFCs) previously requested and acquired by tenants. The latter are likely to request extension of their already acquired, deployed, and running dedicated slices to embed additional networking functions to handle for instance new application flows requiring additional classification, authentication, authorization, processing, traffic steering, etc. The tenants (or end-user service providers) are also likely to introduce gradually their services as needs arise and as their consumer base and profiles evolve. Increasing traffic load often will also require extension of the service graphs and chaining such as introducing additional load balancers and servers, new security functions, and simply new VNFs related to new tenant services. The related service graph extension problem is addressed first through an ILP algorithm that serves as a reference for performance comparisons with a set of proposed heuristic algorithms. A heuristic directly inspired by and based on the ILP and the proposed alternative approaches are shown to scale much better than the ILP while providing good solutions. The solutions include an adaptation of an eigendecomposition approach that provides very good performance for highly connected graphs. The problem is also cast into the well know Steiner Tree search problem whose complexity and performance are formally characterized in the literature. The Steiner based algorithm is shown to provide the best overall tradeoff (in rejection rate, complexity, and quality) with performance closest to optimal.

中文翻译：

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动态 VNF 转发图扩展算法

本文提出了一组算法来扩展租户先前请求和获取的最初部署的虚拟化网络功能转发图（VNF-FG 或服务功能链 - SFC）。后者可能会请求扩展其已经获得、部署和运行的专用切片，以嵌入额外的网络功能，以处理例如需要额外分类、身份验证、授权、处理、流量控制等的新应用程序流。 -用户服务提供商）也可能会随着需求的出现以及他们的消费者群和概况的发展而逐渐推出他们的服务。增加流量负载通常还需要扩展服务图和链接，例如引入额外的负载平衡器和服务器、新的安全功能、以及与新租户服务相关的新 VNF。相关的服务图扩展问题首先通过 ILP 算法解决，该算法用作与一组建议的启发式算法进行性能比较的参考。直接受 ILP 启发并基于 ILP 的启发式算法和提议的替代方法显示出比 ILP 更好的扩展性，同时提供良好的解决方案。这些解决方案包括对特征分解方法的改编，该方法为高度连接的图提供了非常好的性能。该问题也被转换为众所周知的 Steiner Tree 搜索问题，其复杂性和性能在文献中得到了正式描述。显示基于 Steiner 的算法提供了最佳的整体权衡（拒绝率、复杂性和质量），性能最接近最佳。