In Software Defined Networks (SDNs), flows usually request to be processed by a service chain (an ordered set of virtualized network services). SDN-enabled networks manage the routing and processing of flows by a large number of associated finer-granularity rules. These rules are maintained by switches in their local hardware such as Ternary Content Addressable Memories (TCAMs), which support high-speed parallel lookup on wildcard patterns. However, the capacity of hardware switches is limited to thousands because of their high requirements for cost and power. In order to avoid much slower matching by using software switches or even packet loss, we can group flows so that all matching rules can be placed in hardware switches. In such a grouping, all flows in each group match only one rule and will be forwarded to the same routing path, instead of each flow matching one rule. This will result in a longer delay because of processing by the longer newly-grouped service chain. In this paper, we efficiently group flows to minimize the total cost while satisfying the capacity constraint of the forwarding tables in hardware switches. We first prove the submodularity of our objective function and propose a corresponding performanceguaranteed solution. Additionally, we design an efficient heuristic solution based on the classic k-means algorithm. Furthermore, we include discussions on dynamic network situations (insertion, deletion, and update of flows) and an alternative objective. We also conduct real experiments on our testbed to indicate the practicality of our motivation. Extensive simulations are conducted to evaluate the performance of our proposed algorithms.

中文翻译：

---

在基于 NFV 的网络中对多个流的服务链进行分组

在软件定义网络 (SDN) 中，流通常请求由服务链（一组有序的虚拟化网络服务）处理。支持 SDN 的网络通过大量相关的细粒度规则来管理流的路由和处理。这些规则由其本地硬件中的交换机维护，例如支持通配符模式的高速并行查找的三元内容可寻址内存 (TCAM)。然而，硬件交换机的容量限制在数千，因为它们对成本和功率的要求很高。为了避免使用软件交换机进行更慢的匹配甚至丢包，我们可以对流进行分组，以便所有匹配规则都可以放在硬件交换机中。在这样的分组中，每个组中的所有流只匹配一个规则，并将转发到相同的路由路径，而不是每个流都匹配一个规则。这将导致更长的延迟，因为由更长的新分组服务链进行处理。在本文中，我们有效地对流进行分组以最小化总成本，同时满足硬件交换机中转发表的容量约束。我们首先证明了目标函数的子模块性，并提出了相应的性能保证解决方案。此外，我们设计了一种基于经典 k-means 算法的高效启发式解决方案。此外，我们还讨论了动态网络情况（流的插入、删除和更新）和替代目标。我们还在我们的测试平台上进行了真实的实验，以表明我们动机的实用性。进行了广泛的模拟以评估我们提出的算法的性能。