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

Victor Parque*, Tomoyuki Miyashita

*この研究の対応する著者

研究成果: Conference contribution

抄録

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.

本文言語English
ホスト出版物のタイトルProceedings of the 2021 15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021
編集者Sukhan Lee, Hyunseung Choo, Roslan Ismail
出版社Institute of Electrical and Electronics Engineers Inc.
ISBN(電子版)9780738105086
DOI
出版ステータスPublished - 2021 1 4
イベント15th International Conference on Ubiquitous Information Management and Communication, IMCOM 2021 - Seoul, Korea, Republic of
継続期間: 2021 1 42021 1 6

出版物シリーズ

名前Proceedings 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
国/地域Korea, Republic of
CitySeoul
Period21/1/421/1/6

ASJC Scopus subject areas

  • 人工知能
  • コンピュータ ネットワークおよび通信
  • コンピュータ サイエンスの応用
  • 情報システム
  • 情報システムおよび情報管理
  • 健康情報学

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