  Static mapping is the assignment of parallel processes to the processing
elements (PEs) of a parallel system, where the assignment does not change
during the application's lifetime. In our scenario we model an application's
computations and their dependencies by an application graph. This graph is
first partitioned into (nearly) equally sized blocks. These blocks need to
communicate at block boundaries. To assign the processes to PEs, our goal is to
compute a communication-efficient bijective mapping between the blocks and the
PEs.
  This approach of partitioning followed by bijective mapping has many degrees
of freedom. Thus, users and developers of parallel applications need to know
more about which choices work for which application graphs and which parallel
architectures. To this end, we not only develop new mapping algorithms (derived
from known greedy methods). We also perform extensive experiments involving
different classes of application graphs (meshes and complex networks),
architectures of parallel computers (grids and tori), as well as different
partitioners and mapping algorithms. Surprisingly, the quality of the
partitions, unless very poor, has little influence on the quality of the
mapping.
  More importantly, one of our new mapping algorithms always yields the best
results in terms of the quality measure maximum congestion when the application
graphs are complex networks. In case of meshes as application graphs, this
mapping algorithm always leads in terms of maximum congestion AND maximum
dilation, another common quality measure.
