Priority Queue Sorting and Labeled Trees

The priority queue discussed in this talk is an abstract data type supporting theoperations INSERT and DELETEMIN, which transforms an input permutation σ oflength n to an output permutation τ . Atkinson and Thiyagarajah [2] proved that suchpairs (σ, τ) are counted by (n + 1)n−1. This is also well known as Cayley’s formulain graph theory, which counts the number of labeled trees of n vertices. In this talk,I will introduce several bijections between pairs (σ, τ) and labeled trees, and somerelated enumerative and algorithmic results in [1, 2, 3, 4, 5]. References[1] M.D. Atkinson and R. Beals, Priority queues and permutations, SIAM J. Comput. 23(1994) 1225–1230.[2] M.D. Atkinson and M. Thiyagarajah, The permutational power of a priority queue,BIT 33 (1993) 2–6.[3] A.M. Hamel, Priority queue sorting and labeled trees, Annals of Combinatorics, 7(2003) 49–54.[4] I.M. Gessel and K.-Y. Wang, A bijective approach to the permutational power of apriority queue, unpublished.[5] M. Golin and S. Zaks, Labelled trees and pairs of input-output permutations in priorityqueues, Theoret. Comput. Sci. 205 (1998) 99–114.