  Execution graphs of parallel loop programs exhibit a nested, repeating
structure. We show how such graphs that are the result of nested repetition can
be represented by succinct parametric structures. This parametric graph
template representation allows us to reason about the execution graph of a
parallel program at a cost that only depends on the program size. We develop
structurally-parametric polynomial-time algorithm variants of maximum flows.
When the graph models a parallel loop program, the maximum flow provides a
bound on the data movement during an execution of the program. By reasoning
about the structure of the repeating subgraphs, we avoid explicit construction
of the instantiation (e.g., the execution graph), potentially saving an
exponential amount of memory and computation. Hence, our approach enables
graph-based dataflow analysis in previously intractable settings.
