An Efficient Scheme for the Generation of Ordered Trees in Constant Amortized Time

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationProceedings of the 2021 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021
EditorsSukhan Lee, Hyunseung Choo, Roslan Ismail
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9780738105086
DOIs
Publication statusPublished - 2021 Jan 4
Event15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021 - Seoul, Korea, Republic of
Duration: 2021 Jan 42021 Jan 6

Publication series

NameProceedings of the 2021 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021

Conference

Conference15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021
Country/TerritoryKorea, Republic of
CitySeoul
Period21/1/421/1/6

Keywords

  • algorithms
  • Catalan numbers
  • catalan trees
  • combinatorial objects
  • constant amortized time
  • encoding
  • enumeration
  • graphs
  • lattice paths
  • ordered trees
  • plane trees

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Computer Science Applications
  • Information Systems
  • Information Systems and Management
  • Health Informatics

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