@inproceedings{b5b12153cf0f4e85906a53557eac38b1,
title = "An Efficient Scheme for the Generation of Ordered Trees in Constant Amortized Time",
abstract = "Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In combinatorial optimization, generating ordered trees is relevant to evaluate candidate combinatorial objects. In this paper, we present an algebraic scheme to generate ordered trees with $n$ vertices with utmost efficiency; whereby our approach uses $O$ (n) space and $O$ (1) time in average per tree. Our computational studies have shown the feasibility and efficiency to generate ordered trees in constant time in average, in about one tenth of a millisecond per ordered tree. Due to the 1-1 bijective nature to other combinatorial classes, our approach is favorable to study the generation of binary trees with $n$ external nodes, trees with $n$ nodes, legal sequences of $n$ pairs of parentheses, triangulated n-gons, gambler's sequences and lattice paths. We believe our scheme may find its use in devising algorithms for planning and combinatorial optimization involving Catalan numbers.",
keywords = "Catalan numbers, algorithms, catalan trees, combinatorial objects, constant amortized time, encoding, enumeration, graphs, lattice paths, ordered trees, plane trees",
author = "Victor Parque and Tomoyuki Miyashita",
note = "Funding Information: ACKNOWLEDGMENT This research was supported by JSPS KAKENHI Grant Number 20K11998. Publisher Copyright: {\textcopyright} 2021 IEEE.; 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021 ; Conference date: 04-01-2021 Through 06-01-2021",
year = "2021",
month = jan,
day = "4",
doi = "10.1109/IMCOM51814.2021.9377349",
language = "English",
series = "Proceedings of the 2021 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
editor = "Sukhan Lee and Hyunseung Choo and Roslan Ismail",
booktitle = "Proceedings of the 2021 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021",
}