We consider a fundamental update problem of avoiding forwarding loops based on the node-ordering protocol in Software Defined Networks (SDNs). Due to the distributed data plane, forwarding loops may occur during the updates and influence the network performance. The node-ordering protocol can avoid such forwarding loops by controlling the update orders of the switches and does not consume extra flow table space overhead. However, an $\Omega (n)$ lower bound on the number of rounds required by any algorithm using this protocol with loop-free constraint has been proved, where $n$ is the number of switches in the network. To accelerate the updates, a weaker notion of loop-freedom — relaxed loop-freedom — has been introduced. Despite that, the theoretical bound of the node-ordering protocol with relaxed loop-free constraint remains unknown yet. In this article, we solve a long-standing open problem: how to derive $\omega (1)$ -round lower bound or to show that $O(1)$ -round schedules always exist for the relaxed loop-free update problem. Specifically, we prove that any algorithm needs $\Omega (\log n)$ rounds to guarantee relaxed loop freedom in the worst case. In addition, we develop a fast relaxed loop-free update algorithm named Savitar that touches the tight lower bound. For any update instance, Savitar can use at most $2 \lfloor \log _{2}\,\,n \rfloor - 1$ rounds to schedule relaxed loop-free updates. Extensive experiments on Mininet using a Floodlight controller show that Savitar can significantly decrease the update time, achieve near optimal performance and save over 30% of the rounds compared with the state of the art.

中文翻译：

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在SDN的下限内安排轻松的无循环更新

我们考虑一个基本的更新问题，即避免基于软件定义网络（SDN）中的节点排序协议的转发循环。由于分布式数据平面，更新期间可能会发生转发循环并影响网络性能。节点排序协议可以通过控制交换机的更新顺序来避免此类转发循环，并且不会消耗额外的流表空间开销。但是， $ \ Omega（n）$ 已证明使用此协议且无循环约束的任何算法所需的回合数的下限，其中 $ n $ 是网络中的交换机数量。为了加快更新速度，引入了一个较弱的循环自由概念-宽松的循环自由。尽管如此，具有放松的无环约束的节点排序协议的理论界限仍然未知。在本文中，我们解决了一个长期存在的开放性问题：如何得出 $ \ omega（1）$ -舍入下限或显示 $ O（1）$ 对于宽松的无循环更新问题，始终存在全程计划。具体来说，我们证明任何算法都需要 $ \ Omega（\ log n）$ 在最坏的情况下舍入以确保宽松的循环自由。此外，我们开发了一种名为Savitar的快速轻松的无循环更新算法，该算法触及了紧密的下限。对于任何更新实例，Savitar最多只能使用 $ 2 \ lfloor \ log _ {2} \，\，n \ rfloor-1 $ 回合以计划轻松的无循环更新。使用Floodlight控制器在Mininet上进行的大量实验表明，与现有技术相比，Savitar可以显着减少更新时间，达到近乎最佳的性能，并节省超过30％的回合。