Article ID: | iaor20023055 |
Country: | United States |
Volume: | 2 |
Issue: | 1 |
Publication Date: | Jan 1995 |
Journal: | Electronic Journal of Combinatorics |
Authors: | Atkinson M.D., Linton S.A., Walker L.A. |
Keywords: | sets |
A priority queue, a container data structure equipped with the operations insert and delete-minimum, can re-order its input in various ways, depending both on the input and on the sequence of operations used. If a given input σ can produce a particular output τ then (σ,τ) is said to be an allowable pair. It is shown that allowable pairs on a fixed multiset are in one-to-one correspondence with certain k-way trees and, consequently, the allowable pairs can be enumerated. Algorithms are presented for determining the number of allowable pairs with a fixed input component, or with a fixed output component. Finally, generating functions are used to study the maximum number of output components with a fixed input component, and a symmetry result is derived.