An Optimal Single-Path Routing Algorithm in the Datacenter Network DPillar

TL;DR

This paper introduces an optimal, efficient single-path routing algorithm for the DPillar datacenter network, leveraging its Cayley graph structure to improve path length, throughput, and latency.

Contribution

The paper proves DPillar's graph is a Cayley graph, enabling a simple, optimal routing algorithm with linear time complexity and improved performance over previous methods.

Findings

The routing algorithm computes shortest paths in O(k) time.

Empirical results show improved average path length, throughput, and latency.

DPillar's structure allows for significant combinatorial optimization.

Abstract

DPillar has recently been proposed as a server-centric datacenter network and is combinatorially related to (but distinct from) the well-known wrapped butterfly network. We explain the relationship between DPillar and the wrapped butterfly network before proving that the underlying graph of DPillar is a Cayley graph; hence, the datacenter network DPillar is node-symmetric. We use this symmetry property to establish a single-path routing algorithm for DPillar that computes a shortest path and has time complexity $O(k)$, where $k$ parameterizes the dimension of DPillar (we refer to the number of ports in its switches as $n$). Our analysis also enables us to calculate the diameter of DPillar exactly. Moreover, our algorithm is trivial to implement, being essentially a conditional clause of numeric tests, and improves significantly upon a routing algorithm earlier employed for DPillar. Furthermore, we provide empirical data in order to demonstrate this improvement. In particular, we empirically show that our routing algorithm improves the average length of paths found, the aggregate bottleneck throughput, and the communication latency. A secondary, yet important, effect of our work is that it emphasises that datacenter networks are amenable to a closer combinatorial scrutiny that can significantly improve their computational efficiency and performance.