O (log over(m, -) . log N) routing algorithm for (2 log N - 1)-stage switching networks and beyond

Abstract

This paper addresses routing algorithm for a classic network called rearrangeable network with a complexity which is minimum than any other reported algorithms in this class. A new routing algorithm is presented for symmetric rearrangeable networks built with 2 × 2 switching elements. This new algorithm is capable of connection setup for partial permutation, over(m, -) = ρ N, where N is the total input numbers and over(m, -) is the number of active inputs. Overall the serial time complexity of this method is O (N log N)1 1 All log in this paper are base-2. and O (over(m, -) . log N) where all N inputs are active and with over(m, -) < N active inputs respectively. The time complexity of this algorithm in a parallel machine with N completely connected processors is O (log2 N). With over(m, -) active requests the time complexity goes down to O (log over(m, -) . log N), which is better than the O (log2 over(m, -) + log N), reported in the literature for 2frac(1, 2) [(log2 N - 4 log N)frac(1, 2) - log N] ≤ ρ ≤ 1. In later half of this paper, modified rearrangeable networks have been demonstrated built with bigger switching elements (> 2 × 2) with shorter network depth. Routing algorithm for these new networks have been proposed by modifying the proposed algorithm for smaller switching elements networks. Also we shall look into the application of these networks in optical domain for crosstalk free routing.