PSA: in graph theory, the diameter of a network is the length of the longest shortest-path between any pair of nodes. (i.e., out of all the shortest paths between any pair of nodes, return the longest.)<p>It’s a natural generalization of its definition for circles because, if you modeled a disk as abitrarily many nodes that connect to their immediate neighbors, the definitions would be equivalent.<p>Not sure if this is too well known to post.
For some reason the above URL doesn't include a link to the paper [1], just the embedded video [2] of Torsten's talk MSR posted a few days ago and a link to the slides; however, this URL includes everything (slides, video, and paper too): <a href="https://htor.inf.ethz.ch/publications/index.php?pub=187" rel="nofollow">https://htor.inf.ethz.ch/publications/index.php?pub=187</a><p>[1] Slim Fly: A Cost Effective Low-Diameter Network
Topology (2014) [pdf]
<a href="https://htor.inf.ethz.ch/publications/img/sf_sc_2014.pdf" rel="nofollow">https://htor.inf.ethz.ch/publications/img/sf_sc_2014.pdf</a><p>[2] Network Topologies for Large-scale Datacenters: It's the Diameter, Stupid! (2016) [video] <a href="https://www.youtube.com/watch?v=F8F0JN6X0fE" rel="nofollow">https://www.youtube.com/watch?v=F8F0JN6X0fE</a>
What is really missing here is that you can build modular switches out of multiple chips that are a lot more cost effective than connecting single chip boxes mostly because the internal links in a modular chassis in connectors are a lot more cost effective than any cable or optics. This makes the Clos topology with Top or Rack using copper cables and spines out of modular switches with up to 576x100G ports in today's technology winners every time for datacenters. The supercomputing world is still stuck in requirements of extreme low latency and hence hitched to Infiniband or other specialty networks with devices with low number of ports.
AFAIU one major advantage of Clos/fat tree networks is that you'll do quite fine even with relatively dumb static routing protocols.<p>Slim Fly, Dragonfly, and other fancy network topologies tend to require adaptive non-minimal routing to handle adversarial traffic patterns, which Infiniband (or ethernet, for that matter) doesn't support.
I'll just leave this here <a href="https://en.m.wikipedia.org/wiki/Butterfly_network" rel="nofollow">https://en.m.wikipedia.org/wiki/Butterfly_network</a>