Publications and Research
Document Type
Article
Publication Date
2008
Abstract
Binary trees are very useful tools in computer science for estimating the running time of so-called comparison based algorithms, algorithms in which every action is ultimately based on a prior comparison between two elements. For two given algorithms A and B where the decision tree of A is more balanced than that of B, it is known that the average and worst case times of A will be better than those of B, i.e., ₸A(n) ≤₸B(n) and TWA (n)≤TWB (n). Thus the most balanced and the most imbalanced binary trees play a main role. Here we consider them as semilattices and characterize the most balanced and the most imbalanced binary trees by topological and categorical properties. Also we define the composition of binary trees as a commutative binary operation, *, such that for binary trees A and B, A * B is the binary tree obtained by attaching a copy of B to any leaf of A. We show that (T,*) is a commutative po-monoid and investigate its properties.
Comments
This article originally appeared in Applied General Topology, available at DOI: https://doi.org/10.4995/agt.2008.1863
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.