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

AbstractA sequence of priority queue operations can transform a permutation π of n elements to some, but not necessarily all, permutations σ. A recent result of Atkinson and Thiyagarajah (1993) states that the number of distinct transformation pairs (π, σ) 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