Toward a Lower Bound for Sorting Networks

Abstract

A sorting network for N items, or an N-sorter, is a circuit with inputs I = {i₁, i₂, ..., i_N} and outputs Ø = {o₁, o₂, ..., o_N}, such that Ø is a monotonically increasing permutation of I. Sorting networks can be constructed using ranks of a basic cell called a comparator, which is essentially a 2-sorter. For example, the 4-sorter depicted in Fig. 1 employs five comparators, which all emit their larger input on their higher output lead.