Software architectures for Petascale computing will require management
of in excess of a hundred thousand cooperating process-like entities.
One representation that has been suggested for describing such systems
is that of the "workflow", where the required activity is described in
the form of a graph in which nodes represent computations and edges
represent data transfers.  While it is rare at present to see a
workflow of more than a few hundred nodes, one can imagine larger
instances, and these may have some relevance to Petaflops computing
applications.  In an earlier era of parallel computing, such graphical
representations of programs were studied extensively in the form of
Petri Nets, graph reduction engines and dataflow computations.  This
presentation will investigate whether any lessons can be drawn from
the latter research for future software architectures for Petascale
computing.  In particular, the talk will focus on management issues in
large-scale graphs.