A study of the permutation capability of a binary hypercube under deterministic dimension-order routing

A study of the permutation capability of a binary hypercube under the commonly used dimension-order routing is presented. Two modes of the basic routing algorithm have been explored based on non-skipping or skipping identical bits in source and destination addresses when adjusting a route. All the study was done computationally. It has been found that the skip mode in comparison with the non-skip one provides better permutation capability; its beneficial effect on low-dimensional hypercubes, especially concerned with the routing of the so called BPC (bit-permute-complement) permutations, is evident. The possibility of conflict-free routing of the most frequently used permutations under dimension-order routing was also tested.