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Advances in Intelligent Systems and Applications - Volume 1 pp 97–106Cite as

Ranking and Unranking Algorithms for Loopless Generation of Non-regular Trees

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Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 20))

Abstract

A non-regular tree T with a prescribed branching sequence (s 1,s 2,…,s n ) is an ordered tree whose internal nodes are numbered from 1 to n in preorder such that every node i in T has s i children. Recently, Wu et al. (2010) introduced a concise representation called RD-sequences to represent all non-regular trees and proposed a loopless algorithm for generating all non-regular trees in a Gray-code order. In this paper, based on such a Gray-code order, we present efficient ranking and unranking algorithms of non-regular trees with n internal nodes. Moreover, we show that each of the algorithms can be run in \({\mathcal O}(n^2)\) time provided a preprocessing takes \({\mathcal O}(n^2S_{n-1})\) time and space in advance, where \(S_{n-1}=\sum_{i=1}^{n-1}(s_i-1)\).

This work was partially supported by the National Science Council of Taiwan under contracts NSC101-2221-E-262-020 and NSC101-2115-M-141-001.

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Author information

Authors and Affiliations

  1. Department of Industrial Management, Lunghwa University of Science and Technology, Taoyuan, Taiwan, ROC

    Ro-Yu Wu

  2. Institute of Information and Decision Sciences, National Taipei College of Business, Taipei, Taiwan, ROC

    Jou-Ming Chang & An-Hang Chen

  3. Institute of Information Science, Academia Sinica, Taipei, Taiwan, ROC

    Ming-Tat Ko

Authors
  1. Ro-Yu Wu
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  2. Jou-Ming Chang
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  3. An-Hang Chen
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  4. Ming-Tat Ko
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Editor information

Editors and Affiliations

  1. , Department of Computer Science and, National Dong Hwa University, #1, Sec. 2, Da Hsueh Rd., Hualien, Taiwan R.O.C.

    Ruay-Shiung Chang

  2. , Adjunct Professor, University of Canberra, Kirinari St. Mail Room, ACT, 2601, Australia

    Lakhmi C. Jain

  3. , Department of Computer Science and, National Dong Hwa University, #1, Sec. 2, Da Hsueh Rd., Hualien, Taiwan R.O.C.

    Sheng-Lung Peng

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Wu, RY., Chang, JM., Chen, AH., Ko, MT. (2013). Ranking and Unranking Algorithms for Loopless Generation of Non-regular Trees. In: Chang, RS., Jain, L., Peng, SL. (eds) Advances in Intelligent Systems and Applications - Volume 1. Smart Innovation, Systems and Technologies, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35452-6_12

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  • DOI: https://doi.org/10.1007/978-3-642-35452-6_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35451-9

  • Online ISBN: 978-3-642-35452-6

  • eBook Packages: EngineeringEngineering (R0)

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