Operations on data cannot be done entirely independently, but data
can be partitioned into two subsets such that all operations on a
subset can run in parallel.
Solvers for partial differential equations can often be modified to
follow this pattern. For example, for a 2D grid with only
nearest-neighbor communication, it may be possible to treat the grid
as a checkerboard, and alternate between updating red squares and
Another context is staggered grid (“leap frog”) Finite Difference
Time Domain (FDTD solvers, which naturally fit the pattern.
Dependencies between items form a bipartite graph.
Alternate between updating one subset and then the other subset.
Apply the elementwise pattern to each subset.