One classical sorting algorithm, whose performance in many cases remains unanalyzed, is Shellsort. Let ?i be a t-component vector of positive integers. An z-Shellsort will sort any given n elements in t passes, by means of comparisons and exchanges of elements. Let S;(c;n) denote the average number of element exchanges in the j-th J pass, assuming that all the n! initial orderings are equally likely. In this paper we derive asymptotic formulas of Sj(<;n) for any fixed h' = (h,k,l) , making use… Expand

A complete analysis is given of the number of exchanges used by the well-known Batcher’s odd-even merging (and sorting) networks, finding the ratio of exchanges to comparisons approaches 1, although convergence to this asymptotic maximum is very slow.Expand

It is highly desirable to have a method with the speed characteristics of the merging by pairs and the space characteristics of sifting, if such a method were available, to sort twice as many items at one time in the machine and still do it at a reasonably high speed.Expand

IT will be recalled that this volume first made its appearance in 1917. After a reprint in 1925, a second edition followed eight years later, and this was also reprinted in due course. It contained a… Expand

Theory of Functions of Real VariablesBy Prof. Henry P. Thielman. (Prentice-Hall Mathematics Series.) Pp. xiii + 209. (London: Butterworths Scientific Publications, 1953.) 35s. net.Principles of… Expand