Software Implementations

Abstract

A sorting algorithm, in software, is usually described as re-arranging an array of N keys. Each comparator in the sorting network hardware can be implemented in software as a call, C(Lo, Hi), to a subroutine that compares K[Lo] with K[Hi] and swaps them if K[Lo] > K[Hi]—K is a global array of keys and index Lo is less than index Hi in each call. Software representations of sorting networks are shown with diagrams that we call Knuth diagrams . Each key-index in the array being sorted is represented by a horizontal line in the Knuth diagram and each subroutine call, C(Lo, Hi), is represented by a vertical line between the horizontal lines of the Lo and Hi indices. Permuting the locations of the keys generates a re-labeled software program or Knuth diagram for a given sorting network. Though it looks different, the re-labeled version of the network is equivalent to the original version. However, since it looks different, the re-labeled network can help us better understand the behavior of the sorting network and this can help us discover even better networks.