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

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

Routing algorithms for recursively-defined data centre networks

The server-centric data centre network architecture can accommodate a wide variety of network topologies. Newly proposed topologies in this arena often require several rounds of analysis and experimentation in order that they might achieve their full potential as data centre networks. We propose a family of novel routing algorithms on two well-known data centre networks of this type, (Generalized) DCell and FiConn, using techniques that can be applied more generally to the class of networks we call completely connected recursively-defined networks. In doing so, we develop a classification of all possible routes from server-node to server-node on these networks, called general routes of order t, and find that for certain topologies of interest, our routing algorithms efficiently produce paths that are up to 16% shorter than the best previously known algorithms, and are comparable to shortest paths. In addition to finding shorter paths, we show evidence that our algorithms also have good load-balancing properties

An efficient shortest path routing algorithm in the data centre network DPillar

DPillar has recently been proposed as a server-centric data centre network and is combinatorially related to the well-known wrapped butterfly network. We explain the relationship between DPillar and the wrapped butterfly network before proving a symmetry property of DPillar. We use this symmetry property to establish a single-path routing algorithm for DPillar that computes a shortest path and has time complexity O(klog(n))O(klog⁡(n)), where k parameterizes the dimension of DPillar and n the number of ports in its switches. 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. A secondary and important effect of our work is that it emphasises that data centre networks are amenable to a closer combinatorial scrutiny that can significantly improve their computational efficiency and performance

Relating the bisection width of dual-port, server-centric datacenter networks and the solution of edge-isoperimetric problems in graphs

Stellar datacenter networks are a recent generic construction designed to transform a base-graph into a dual-port, server-centric datacenter network. We prove that the S-bisection width of any stellar datacenter network can be obtained from the solution of isoperimetric problems on the base-graph, provided that the base-graph is regular. We extend previous research on the stellar datacenter networks GQ⁎, instantiated with generalized hypercubes, and show that with respect to S-bisection width, GQ⁎ performs well in comparison with the dual-port datacenter network FiConn. Our work develops a strong combinatorial link between graph bisection width and throughput metrics for stellar datacenter networks

Realistic evaluation of interconnection network performance at high loads

Any simulation-based evaluation of an interconnection network proposal requires a good characterization of the workload. Synthetic traffic patterns based on independent traffic sources are commonly used to measure performance in terms of average latency and peak throughput. As they do not capture the level of self-throttling that occurs in most parallel applications, they can produce inaccurate throughput estimates at high loads. Thus, workloads that resemble the varying levels of synchronization of actual applications are needed to study the performance of interconnection networks. One approach is to use simple, burst-synchronized synthetic workloads that emulate the self-throttling of many parallel applications. To validate this approach, we compare the gains achieved by a restrictive injection mechanism under this workload with those obtained using traces from the NAS Parallel Benchmarks. This study confirms that the burst-synchronized traffic model provides reasonable performance estimates, which could be improved by taking into account dependency chains between messages.Ridruejo, F.J., Navaridas, J., Miguel-Alonso, J. and Izu, C

The stellar transformation: from interconnection networks to datacenter networks

The first dual-port server-centric datacenter network, FiConn, was introduced in 2009 and there are several others now in existence; however, the pool of topologies to choose from remains small. We propose a new generic construction, the stellar transformation, that dramatically increases the size of this pool by facilitating the transformation of well-studied topologies from interconnection networks, along with their networking properties and routing algorithms, into viable dual-port server-centric datacenter network topologies. We demonstrate that under our transformation, numerous interconnection networks yield datacenter network topologies with potentially good, and easily computable, baseline properties. We instantiate our construction so as to apply it to generalized hypercubes and obtain the datacenter networks GQ⋆. Our construction automatically yields routing algorithms for GQ⋆ and we empirically compare GQ⋆ (and its routing algorithms) with the established datacenter networks FiConn and DPillar (and their routing algorithms); this comparison is with respect to network throughput, latency, load balancing, fault-tolerance, and cost to build, and is with regard to all-to-all, many all-to-all, butterfly, random, hot-region, and hot-spot traffic patterns. We find that GQ⋆ outperforms both FiConn and DPillar (sometimes significantly so) and that there is substantial scope for our stellar transformation to yield new dual-port server-centric datacenter networks that are a considerable improvement on existing ones