Setup Algorithms for Cube-Connected Parallel Computers Using Recursive Karnaugh Maps

This paper presents optimal setup procedures for cubeconnected networks. The setup patterns include paths, transpositions, cycles, and one-pass permutations. For an N-input cube-connected network, the procedure for paths requires O(log2 N ) steps, and O(N) space, that for transpositions and cycles requires O(N) steps, and O(N) space, and that for permutations takes O(N log2 N ) steps, and O(N) space. Furthermore, the time complexities of the setup procedures for transpositions, cycles, and permutations can be improved as O(log2 N ) by using O(N) processors.