Optimal networks from error correcting codes

Abstract

To address growth challenges facing large Data Centers and supercomputing clusters a new construction is presented for scalable, high throughput, low latency networks. The resulting networks require 1.5-5 times fewer switches, 2-6 times fewer cables, have 1.2-2 times lower latency and correspondingly lower congestion and packet losses than the best present or proposed networks providing the same number of ports at the same total bisection. These advantage ratios increase with network size.The key new ingredient is the exact equivalence discovered between the problem of maximizing network bisection for large classes of practically interesting Cayley graphs and the problem of maximizing codeword distance for linear error correcting codes. Resulting translation recipe converts existent optimal error correcting codes into optimal throughput networks.Ethernet implementation was developed and a prototype built using managed COTS switches. Integrated control plane handles topology, distribution of forwarding tables and fault recovery. Scalable routing uses stretch-free topological addressing. Local load balancing distributes flows at the source over multiple, nonminimal, edge disjoint paths. Path selection does not use tunneling or overlays but embeds path selectors in the topological addresses resulting in wire-speed forwarding and allowing for cut-through switching where available.

Measuring and Understanding Throughput of Network Topologies

“…We find the three expanders have nearly identical performance for uniform traffic (e.g. all-to-all); this differs from conclusions of [5], [42] which analyzed bisection bandwidth rather than throughput. We find that expanders significantly outperform fat trees; this differs from the results of [48] which concluded that fat trees perform as well or better.…”

“…Similar trends are observed under all-to-all and random matching workloads. The paper [42] claimed high performance (in terms of bisection bandwidth) with substantially less equipment than past designs, but we find that while Long Hop networks do have high performance, they are no better than random graphs, and sometimes worse.…”

“…Performance depends on randomness in the construction, but at larger sizes, performance differences between Jellyfish instances are minimal (≈ 1%). [42] In Figure 8, we show that the relative throughput of Long Hop networks approaches 1 at large sizes under the longest matching TM. Similar trends are observed under all-to-all and random matching workloads.…”

“…3) Topologies: Our evaluation uses 10 families of computer networks. Topology families evaluated are: BCube [17], DCell [18], Dragonfly [25], Fat Tree [30], Flattened butterfly [24], Hypercubes [6], HyperX [2], Jellyfish [39], Long Hop [42] and Slim Fly [5]. For evaluating the cut-based metrics in a wider variety of environments, we consider 66 non-computer networks -food webs, social networks, and more [1].…”

“…A number of studies (e.g. [2], [10], [41], [42], [46]) employ cut metrics. It has been noted [47] that bisection bandwidth does not always predict average-case throughput (in a limited setting; §V).…”