Some Mathematical Aspects of Data Centre Networks

Iain A. Stewart ( Durham University )

The design of data centre networks is becoming an important aspect of computing provision as software and infrastructure services increasingly migrate to the cloud and the demand for bigger and bigger data centres grows. This design is ordinarily undertaken by network engineers and is usually holistic in that not only is an interconnection topology prescribed but more practical aspects are often encompassed relating to, for example, routing, fault-tolerance and throughput. Consequently, these initial designs, though often impressive, tend to be prototypical with the intention being to demonstrate proof-of-concept and practical viability rather than to detail the finished article. Not only does improving and optimizing data centre networks provide opportunities for theoreticians to delve into their mathematical toolboxes but particular aspects of data centre network design can also lead to new problems that perhaps might not be immediately practically relevant but are interesting in their own right from a theoretical perspective. In this talk I shall introduce some of the practical considerations behind data centre network design and show how different aspects of mathematics impinge on this world; such aspects might include isoperimetric sets within graphs, the utilization of combinatorial design theory and the reduction of core data centre problems to combinatorics.