Merging and Sorting Networks with the Topology of the Omega Network

Abstract

We consider a class of comparator networks obtained from the omega permutation network by replacing each switch with a comparator exchanger of arbitrary direction. These networks are all isomorphic to each other, have merging capabilities, and can be used as building blocks of sorting networks in ways different from the standard merge-sort scheme. It is shown that the bitonic merger and the balanced merger are members of the class. These two networks were not previously known to be isomorphic.