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Extra info for Mathematical Aspects of Scientific Software
FINKEL, Quotient Networks, IEEE Transactions on Computers, Vol. C-31, April, 1982. FORTES, 1. and D. MOLDOVAN, Parallelism Detection and Transformation Techniques Useful for VLSI Algorithms, Iournal of Parallel and Distributed Computing, Vol. 2, August, 1985. GAREY, M. and D.
In PI:ep-P input graphs, the dataflow is implicit in the communication topology and processes are treated as atomic. IFI graphs generally describe the domain of programs which can be represented within single-assignment languages like Sisal ; Prep-P input graphs generally describe the domain of parallel algorithms which may be decomposed into a set of communicating sequential processes. The contrast between algorithm representations dictates different applicable transformations. IF! graphs are amenable to graph expansion so that the internalization transformation operates on an expanded version of the input graph.
We illustrate the graph-based approach with some recent work by Sarkar and Hennessy in mapping dataflow graphs to shared and non-shared memory MIMD architectures (, ). Algorithms are represented in this work by dataflow computation graphs in the IF1 format . An IF1 program is composed of a hierarchy of acyclic dataflow graphs whose nodes are either simple (atomic) or compound. Sarkar and Hennessy map programs in this format into an MIMD multiprocessor model using a sequence of four 48 A Band 1 2 1 2 3 '4 0 1 5 2 7 1 Partitioned index set for y =A· i 9' o J Figure 2 Fortes and Moldovan's  depiction of the mapping of a two-dimensional index space representing a matrix-vector computation.