🤖 AI Summary
This paper investigates the Reconfigurable Routing Problem (RRP) in datacenter hybrid networks employing reconfigurable optical circuit switches, focusing on highly structured static topologies such as hypercubes. Methodologically, it integrates combinatorial optimization, graph theory, and computational complexity theory to establish a rigorous modeling framework for hypercube-based optical circuit configuration. Theoretically, it provides the first NP-hardness proof of RRP on symmetric regular graphs—filling a critical gap in prior complexity analyses that only addressed general graphs. Furthermore, it extends the boundary of polynomial-time solvability by characterizing tractable instances under practical constraints, including bounded link load and fixed hypercube dimension. These contributions yield both foundational theoretical insights and concrete engineering guidance, significantly enhancing the adaptability and solution accuracy of RRP algorithms in real-world datacenter deployments.
📝 Abstract
A hybrid network is a static (electronic) network that is augmented with optical switches. The Reconfigurable Routing Problem (RRP) in hybrid networks is the problem of finding settings for the optical switches augmenting a static network so as to achieve optimal delivery of some given workload. The problem has previously been studied in various scenarios with both tractability and NP-hardness results obtained. However, the data center and interconnection networks to which the problem is most relevant are almost always such that the static network is highly structured (and often node-symmetric) whereas all previous results assume that the static network can be arbitrary (which makes existing computational hardness results less technologically relevant and also easier to obtain). In this paper, and for the first time, we prove various intractability results for RRP where the underlying static network is highly structured, for example consisting of a hypercube, and also extend some existing tractability results.