Setup algorithms for cube-connected parallel computers using recursive Karnaugh maps

Optimal setup procedures for cube-connected networks are described. The setup patterns include paths, transpositions, cycles, and one-pass permutations. It is shown that for an N-input cube-connected network, the procedure for paths requires O(log ₂ N) steps and O(N) space, the procedure for transportations and cycles requires O(N) steps and O(N) space, and the procedure for permutations takes O(N log₂ N) steps and O(N) space. It is also shown that the time complexities of the setup procedures for transpositions, cycles, and permutations can be improved as O(log₂ N) by using O(N) processors