The organization of permutation architectures with bussed interconnections

This paper explores the problem of efficiently permuting data stored in VLSI chips in accordance with a predetermined set of permutations. By connecting chips with shared bus interconnections, as opposed to point-to-point interconnections, we show that the number of pins per chip can often be reduced. For example, for infinitely many n, we exhibit permutation architectures with ⌈√n⌉ pins per chip that can realize any of the n cyclic shifts on n chips in one clock tick. When the set of permutations forms a group with p elements, any permutation in the group can be realized in one clock tick by an architecture with O(√p lg p) pins per chip. When the permutation group is abelian, O(√p) pins suffice. These results are all derived from a mathematical characterization of uniform permutation architectures based on the combinatorial notion of a difference cover.