A Unified Framework to Discover Permutation Generation Algorithms

Abstract

We present two simple, intuitive and general algorithmic frameworks that can be used to design a wide variety of permutation generation algorithms. The frameworks can be used to produce 19 existing permutation algorithms, including the well-known algorithms of Heap, Wells, Langdon, Zaks, Tompkins and Lipski. We use the frameworks to design two new sorting-based permutation generation algorithms, one of which is optimal.