A Tight Lower Bound for Relaxed Loop-Free Updates in SDNs

Hao Zhou, Xiaofeng Gao, Jiaqi Zheng, Guihai Chen

Abstract: Due to the unpredictable update orders in the data plane, a transient forwarding loop may be introduced in Software Defined Networks (SDNs) during the updates, which can result in packet drops and influence the application performance. The node-ordering protocol is a major update mechanism without incurring extra flow table space overhead. Existing algorithms using this protocol with loop-free constraint require Ω(n)-round lower bound, 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. However, many problems about the theoretical bound of the node-ordering protocol with relaxed loop-free constraint remain unsolved yet. In this paper, we provide a rigorous proof to derive a Ω (log n)-round lower bound for relaxed loop-free update problem, which closes a long-term open problem whether O(1)-round schedules always exist or not. In addition, we develop a fast relaxed loop-free update algorithm named Savitar that touches the tight lower bound. Specifically, we prove that Savitar can use at most 2⌊log2 n⌋ - 1 rounds to guarantee relaxed loop-freedom for any update instance. Extensive experiments on Mininet using a Floodlight controller show that Savitar can significantly decrease the update time, achieve the near optimal solution and save the number of rounds over 30% compared with the state of the art.