On generating B-trees with constant average delay and in lexicographic order

Abstract

Gupta, Lee and Wong described algorithms for generating 2–3 trees and B-trees and left as open problems whether algorithms exist that generate them in lexicographic order, and whether it is possible to generate 2–3 trees or B-trees in constant average delay, exclusive of the output. In this note we modify the B-tree representation and show that the order of generating 2–3 trees and B-trees in their paper islexicographic under the new representation. We also prove that their algorithm for generating B-trees has a constant average delay property. This is the first algorithm for which such a property is proved, showing that B-trees can be generated with constant average delay.