Labelled trees and pairs of input-output permutations in priority queues

A sequence of priority queue operations can transform a permutation pi of n elements to some, but not necessarily all, permutations sigma. A recent result of Atkinson and Thiyagarajah (1993) stales that the number of distinct transformation pairs (pi, sigma) is (n + 1)(n-1). By Cayley)s theorem this is also the number of labelled trees with n + 1 nodes. We present a direct correspondence between labelled trees and transformation pairs and a linear time algorithm for constructing the tree corresponding to a pair of permutations along with related results. (C) 1998-Elsevier Science B.V. All rights reserved.