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

✍ Scribed by M. Golin; S. Zaks

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 912 KB
• Volume: 205
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(97)00037-6

✦ Synopsis

A sequence of priority queue operations can transform a permutation 72 of n elements to some, but not necessarily all, permutations 6. A recent result of Atkinson and Thiyagarajah (1993) states that the number of distinct transformation pairs (TC., a) is (n + l)"-'. 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.