An inverted taxonomy of sorting algorithms

Abstract

An alternative taxonomy (to that of Knuth and others) of sorting algorithms is proposed. It emerges naturally out of a top-down approach to the derivation of sorting algorithms. Work done in automatic program synthesis has produced interesting results about sorting algorithms that suggest this approach. In particular, all sorts are divided into two categories: hardsplit/easyjoin and easysplit/hardjoin. Quicksort and merge sort, respectively, are the canonical examples in these categories. Insertion sort and selection sort are seen to be instances of merge sort and quicksort, respectively, and sinking sort and bubble sort are in-place versions of insertion sort and selection sort. Such an organization introduces new insights into the connections and symmetries among sorting algorithms, and is based on a higher level, more abstract, and conceptually simple basis. It is proposed as an alternative way of understanding, describing, and teaching sorting algorithms.