Hilbert graph: an expandable interconnection for clusters

The use of commodity hardware has played an important role in the construction of high performance computers in recent years. In particular this model of computation has become very popular in research groups and organisations due to its favourable price/performance ratio (Becker et al., 1995). Although cluster computing has been very successful for applications consisting of a large number of serial tasks characterised by a low communication cost, the approach has been less successful in the scenario where a small number of tasks with high communication costs need to be executed; such as in multigrid methods and other parallel iterative solvers (Buyya et al., 2002). The Hilbert graph introduced in this work is formed by the superposition of a Hilbert curve with an extended mesh. Nodes are placed along the middle of a segment in the Hilbert curve and the extended mesh is formed by joining nodes with the same horizontal or vertical position. The Hilbert graph has a fixed degree of four, and exhibits a much better support for random communication patterns and an efficient two dimensional layout, while retaining the same cutwidth complexity of a two dimensional torus. Furthermore, it retains the incremental expandability found in the mesh and torus while supporting the increased traffic expected from such expansion much more efficiently.