Generalized parallel delta networks: a new class of rearrangeable interconnection networks

The definition is presented of a class of N×N multistage interconnection networks called generalized parallel delta networks (GPDNs). This class includes the already known replicated delta networks (RDNs) and parallel delta networks (PDNs). For GPDNs, the rearrangeability condition is given and a routing algorithm for the establishment of any set of connection requests is presented. The proposed algorithm operates for GPDNs composed of 2^q×2 ^q switching elements and it is able to set up any permutation with a time complexity equal to O(N log₂ N). The applicability of RDNs, PDNs, and other GPDNs for the implementation of rearrangeable topologies is investigated. In particular, it is proved that if large networks (N>256) have to be implemented, GPDNs require a smaller number of switching elements than RDNs or PDNs