Section: New Results

Scalable mapping onto (disconnected) parts of regular target architectures

Since its inception, Scotch allows one to map graphs onto so-called “algorithmically-defined” target architectures. They are regular architectures such as hypercube, multi-dimensional grids and tori, butterfly networks, etc., whose characteristics are defined by subroutines which are part of the Scotch library. However, on today's large-scale computer systems, software jobs do not usually run on all of the machine, but on a set of nodes assigned by the batch scheduler. Consequently, one should be able to map a process graph onto (possibly disconnected) parts of an algorithmically-defined target architecture, which was not an available feature. Only “decomposition-defined” architectures (another way to represent target architectures in Scotch ) supported this feature, but are not scalable above a few hundred processing elements.

In order to allow Scotch to provide mappings onto parts of an algorithmically-defined target architecture, a new meta target architecture, called “sub ”, has been created. The sub architecture allows one to restrict a regular algorithmically-defined target architecture to a subset of its vertices. Instead of using a top-down approach to build a description of the target architecture, through a recursive bipartitioning algorithm, our new algorithm uses a bottom-up approach, based on recursive matching and coarsening of neighboring vertices, much like for graph coarsening. The clustering tree is pruned of branches that lead to parts of the machine that are not allowed mapping targets. Distance between subdomains is computed using the distance function of the underlying algorithmically-defined target architecture. Preliminary results have been presented at a SIAM CS&E conference workshop [14] , and a beta-version of the upcoming release 6.0.5 of Scotch has been shipped to early testers at Lawrence Livermore National Laboratory.