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Static mapping is the assignment of parallel processes to the processingelements (PEs) of a parallel system, where the assignment does not changeduring the application's lifetime. In our scenario we model an application'scomputations and their dependencies by an application graph. This graph isfirst partitioned into (nearly) equally sized blocks. These blocks need tocommunicate at block boundaries. To assign the processes to PEs, our goal is tocompute a communication-efficient bijective mapping between the blocks and thePEs.  This approach of partitioning followed by bijective mapping has many degreesof freedom. Thus, users and developers of parallel applications need to knowmore about which choices work for which application graphs and which parallelarchitectures. To this end, we not only develop new mapping algorithms (derivedfrom known greedy methods). We also perform extensive experiments involvingdifferent classes of application graphs (meshes and complex networks),architectures of parallel computers (grids and tori), as well as differentpartitioners and mapping algorithms. Surprisingly, the quality of thepartitions, unless very poor, has little influence on the quality of themapping.  More importantly, one of our new mapping algorithms always yields the bestresults in terms of the quality measure maximum congestion when the applicationgraphs are complex networks. In case of meshes as application graphs, thismapping algorithm always leads in terms of maximum congestion AND maximumdilation, another common quality measure.

Algorithms for Mapping Parallel Processes onto Grid and Torus Architectures