Reconfigurable routing in data center networks

TL;DR

The paper investigates the Reconfigurable Routing Problem ($RRP$) in hybrid data center networks, focusing on highly structured static topologies such as hypercubes. It develops a series of NP-hardness results for the case where the dynamic links are restricted (notably $\\delta=1$) and for specific path-segmentation constraints (e.g., $\sigma=1$ and $\sigma=3$), while also identifying polynomial-time solvable regimes (e.g., $1$-switched $RRP$ with $\sigma=0$). A central methodological advance is the introduction of lunar graph classes and reductions from Partial Domination (via RXC3 and 3-Min-Bisection) to obtain hardness results on structured topologies. Collectively, the results show that even in realistically structured data center fabrics, optimally configuring reconfigurable routing remains computationally intractable in many practically relevant regimes, guiding the development of heuristics and approximation approaches.

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.

Figures (11)

• Figure 1: Basic model of an optical wireless data-center network, as described in CSBDRBTS18firefly14ZSXXTC22. Practical timescales for reconfiguration vary from milliseconds firefly14 to microseconds or nanoseconds CSBDRBTS18ZSXXTC22.
• Figure 2: A hybrid network.
• Figure 3: An augmented network and its abstracted dynamic links.
• Figure 4: The graph $D^\prime$.
• Figure 5: Attaching the gadgets.

Theorems & Definitions (40)

• theorem 1
• proof
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• theorem 2
• proof
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• lemma 1: FPS19
• theorem 3
• proof