Abstract
The theory of skewing schemes deals with the problem of distributing data in parallel memories, in such a way that parallel computations can proceed efficiently. Until now skewing schemes have been studied from the viewpoint of the BSP and ILLIAC IV architectures and image processing. In the present paper we are concerned with hierarchically organized parallel memory systems, for which a new class of skewing schemes is introduced, namely the multiperiodic skewing schemes. We show that multiperiodic skewing schemes are an extension of both the periodic skewing schemes and the diamond schemes for traditional parallel memories. It is also shown that the schemes work out very well for many applications and, in particular, a bound on the minimum number of memory banks needed for certain applications is derived. Furthermore, multiperiodic skewing schemes can be represented at the cost of only a small amount of space, which makes them of practical interest.
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