Transiently Consistent SDN Updates: Being Greedy is Hard

TL;DR

This paper investigates the complexity of updating SDN configurations consistently and efficiently, proving NP-hardness for greedy approaches and providing approximation algorithms for specific cases.

Contribution

It proves that computing maximum loop-free SDN updates is NP-hard and offers approximation algorithms for certain instances.

Findings

NP-hardness of greedy SDN update computation

Existence of approximation algorithms for special cases

Implications for the maximum acyclic subgraph problem

Abstract

The software-defined networking paradigm introduces interesting opportunities to operate networks in a more flexible, optimized, yet formally verifiable manner. Despite the logically centralized control, however, a Software-Defined Network (SDN) is still a distributed system, with inherent delays between the switches and the controller. Especially the problem of changing network configurations in a consistent manner, also known as the consistent network update problem, has received much attention over the last years. In particular, it has been shown that there exists an inherent tradeoff between update consistency and speed. This paper revisits the problem of updating an SDN in a transiently consistent, loop-free manner. First, we rigorously prove that computing a maximum (greedy) loop-free network update is generally NP-hard; this result has implications for the classic maximum acyclic subgraph problem (the dual feedback arc set problem) as well. Second, we show that for special problem instances, fast and good approximation algorithms exist.