  In parallel solution of partial differential equations, a complex stencil
update formula that accesses multiple layers of neighboring grid points
sometimes must be decomposed into atomic stages, ones that access only
immediately neighboring grid points. This paper shows that this requirement can
be formulated as constraints of an optimization problem, which is equivalent to
the dual of a minimum-cost network flow problem. An optimized decomposition of
a single stencil on one set of grid points can thereby be computed efficiently.
