Extended Class of Pruned Crossbar Switches for Optical Networks

Reducing crosspoints of conventional pruned crossbar switches (PXBSs) with N2 3 crosspoints, where N is the switch size, was investigated from an architectural point of view. PXBSs have been created by removing parts of 2x2 switching elements (or simply cells) from crossbar switches (XBSs), while preserving both the switches’ planar structure and wide-sense nonblocking property. In this paper, we consider an extended class of PXBSs that has either a 3D structure or rearrangeably nonblocking capability. Two new families of extended PXBSs are described. The first is wide-sense nonblocking; it has a 3D structure of N(N 1) cells. Its form is similar to those of ILLIAC(N, N 1) torus networks and is isomorphic to a degree-four chordal ring. Its switch control complexity becomes O(1) like conventional XBSs. The second has nearly 3N2/4 cells in a planar structure; it is rearrangeably nonblocking and its switch control complexity is O(N). Its maximum number of rearrangements remains three, regardless of N for N 5. It decreases to two, if a pair of input and output ports is left unused. We point out that the second switch provides a missing link between crossbar switches of N2 cells and triangular switches of N(N 1)/2 cells and yields different rearrangeably nonblocking switches, with the number of rearrangements ranging from three to N 2.