  Programs admitting a polyhedral representation can be transformed in many
ways for locality and parallelism, notably loop tiling. Data flow analysis can
then compute dependence relations between iterations and between tiles. When
tiling is applied, certain iteration-wise dependences cross tile boundaries,
creating the need for inter-tile data communication. Previous work computes it
as the flow-in and flow-out sets of iteration tiles.
  In this paper, we propose a partitioning of the flow-out of a tile into the
maximal sets of iterations that are entirely consumed and incur no redundant
storage or transfer. The computation is described as an algorithm and performed
on a selection of polyhedral programs. We then suggest possible applications of
this decomposition in compression and memory allocation.
