Lower bound on the size of shellsort sorting networks

Abstract

Shellsort is a sorting algorithm that is based on a set of parameters called increments. Shellsort has been used both as a sequential sorting algorithms and as a sorting network. The central result of this paper is that all Shellsort sorting networks based on monotonically decreasing increments require Ω(N log2N/log log N) comparators. Previously, only the trivial Ω(N log N) bound was known for this class of networks. The lower bound obtained in this paper nearly matches the upper bound of O(N log2 N) that was proven by Pratt.