Hierarchical Parallel Memory-Systems, and Multi-Periodic Skewing Schemes

摘要

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. In the present paper the authors are concerned with hierarchically organized parallel memory-systems, for which a new class of skewing schemes is introduced, namely the multi-periodic skewing schemes. The authors show that multi-periodic 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, multi-periodic skewing schemes can be represented at the cost of only a small amount of space, which makes them of practical interest.