A heuristic to accelerate in-situ permutation algorithms

In-situ permutation algorithms permute an array of n items without using a second array. Little space is needed when one proceeds permuting along a cycle. Thus, those algorithms first search for one element called the leader on each cycle of the permutation. Then they move the items cycle by cycle. A great fraction of the runtime is spent with testing whether elements are leaders. We present a simple-to-implement heuristic to accelerate the search for leaders and present performance gains for randomly chosen permutations on three algorithms.