O(n) routing in rearrangeable networks

In (2n)1)-stage rearrangeable networks, the routing time for any arbitrary permutation is X(n) compared to its propagation delay O(n) only. Here, we attempt to identify the sets of permutations, which are routable in O(n) time in these networks. We de®ne four classes of self-routable permutations for Benes network. An O(n) algorithm is presented here, that identi®es if any permutation P belongs to one of the proposed self-routable classes, and if yes, it also generates the necessary control vectors for routing P. Therefore, the identi®cation, as well as the switch setting, both problems are resolved in O(n) time by this algorithm. It covers all the permutations that are self-routable by anyone of the proposed techniques. Some interesting relationships are also explored among these four classes of permutations, by applying the concept of Ôgroup-transformationsÕ [N. Das, B.B. Bhattacharya, J. Dattagupta, Hierarchical classi®cation of permutation classes in multistage interconnection networks, IEEE Trans. Comput. (1993) 665±677] on these permutations. The concepts developed here for Benes network, can easily be extended to a class of (2n)1)-stage networks, which are topologically equivalent to Benes network. As a result, the set of permutations routable in a (2n)1)-stage rearrangeable network, in a time comparable to its propagation delay has been extended to a large extent. Ó 2000 Elsevier Science B.V. All rights reserved.