Better Bounds in Networks based on Randomly-Wired Expander

Linear size expanders have been studied in many fields for the practical use, which is possibility to connect large numbers of device chips in parallel communication systems. One major limitation on the efficiency of parallel computer designs has been the prohibitively high cost of parallel communication between processors and memories. Linear size expanders can be used to construct theoretically optimal interconnection networks. In current, the defined constructions have large constant factors, thus rendering them impractical for reasonable sized networks. This paper presents an improvement on constructing concentrators using an $(n,\;k,\;2rs/(r^2-s^2))expander,$ which realizes the reduction of the size in a superconcentrator by a constant factor.