What Price Regularity?

We review various properties of irregular graphs and suggest that they may provide useful maps for connecting processors together in distributed-memory MIMD machines. In particular, for many applications the performance of a system in an irregular configuration can be expected to exceed by far that of systems in standard configurations such as hypercubes and tori, which are poor over many performance measures. Techniques are discussed which allow the construction of near-optimal or optimal graphs with respect to various measures of goodness, including diameter, mean interprocessor distance and worst through-routing load. We conclude that where regularity is not important, irregular graphs will almost always outperform standard, regular ones.