The Use of Information in Sorting

Abstract

The information-gathering aspect of sorting is considered from a theoretical viewpoint. A large class, R, of sorting algorithms is defined, based on the idea of information use. Properties of this algorithm class are developed, and it is noted that several well-known sorting algorithms are closely related to algorithms in R . The Binary Tree Sort is shown to be in R and to have unique properties in this class. A vector is defined which characterizes the information-gathering efficiency of the algorithms of R . Finally, a more general class of algorithms is defined, and some of the definitions extended to this class. Two intriguing conjectures are given which appear to require graph theory or combinatorial topology for their solution.