Load-Optimization in Reconfigurable Networks: Algorithms and Complexity of Flow Routing

摘要

Emerging reconfigurable data centers introduce the unprecedented flexibility in how the physical layer can be programmed to adapt to current traffic demands. These reconfigurable topologies are commonly hybrid, consisting of static and reconfigurable links, enabled by e.g. an Optical Circuit Switch (OCS) connected to top-of-rack switches in Clos networks. Even though prior work has showcased the practical benefits of hybrid networks, several crucial performance aspects are not well understood.In this paper, we study the algorithmic problem of how to jointly optimize topology and routing in reconfigurable data centers with a known traffic matrix, in order to optimize a most fundamental metric, maximum link load. We chart the corresponding algorithmic landscape by investigating both un-/splittable flows and (non-)segregated routing policies. We moreover prove that the problem is not submodular for all these routing policies, even in multi-layer trees, where a topological complexity classification of the problem reveals that already trees of depth two are intractable.However, networks that can be abstracted by a single packet switch (e.g., nonblocking Fat-Tree topologies) can be optimized efficiently, and we present optimal polynomial-time algorithms accordingly. We complement our theoretical results with trace-driven simulation studies, where our algorithms can significantly improve the network load in comparison to the state of the art.