Some properties of ternary trees

Abstract

Ternary search trees and ternary sequence search trees are defined as natural extensions of the binary case. Ternary tree insertion and its relation to topological sorting is also considered as a natural generalisation of binary tree insertion with its relationship to complete sorting. The problem of quasi-topological sorting, which can be regarded as a generalisation of topological sorting, is also solved using ternary trees. A possible definition of topological searching is presented. The analysis of ternary trees is given using recurrence relations.