IEICE TRANSACTIONS on Information
Ranking and Unranking of t-Ary Trees Using RD-Sequences
Summary :
In this paper, we introduce a concise representation, called right-distance sequences (or RD-sequences for short), to describe all t-ary trees with n internal nodes. A result reveals that there exists a close relationship between the representation and the well-formed sequences suggested by Zaks [Lexicographic generation of ordered trees, Theoretical Computer Science 10 (1980) 63-82]. Using a coding tree and its concomitant tables, a systematical way can help us to investigate the structural representation of t-ary trees. Consequently, we develop efficient algorithms for determining the rank of a given t-ary tree in lexicographic order (i.e., a ranking algorithm), and for converting a positive integer to its corresponding RD-sequence (i.e., an unranking algorithm). Both the ranking and unranking algorithms can be run in O(tn) time and without computing all the entries of the coefficient table.
- Publication
- IEICE TRANSACTIONS on Information Vol.E94-D No.2 pp.226-232
- Publication Date
- 2011/02/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E94.D.226
- Type of Manuscript
- Special Section PAPER (Special Section on Foundations of Computer Science -- Mathematical Foundations and Applications of Algorithms and Computer Science --)
- Category
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Ro-Yu WU, Jou-Ming CHANG, Yue-Li WANG, "Ranking and Unranking of t-Ary Trees Using RD-Sequences" in IEICE TRANSACTIONS on Information,
vol. E94-D, no. 2, pp. 226-232, February 2011, doi: 10.1587/transinf.E94.D.226.
Abstract: In this paper, we introduce a concise representation, called right-distance sequences (or RD-sequences for short), to describe all t-ary trees with n internal nodes. A result reveals that there exists a close relationship between the representation and the well-formed sequences suggested by Zaks [Lexicographic generation of ordered trees, Theoretical Computer Science 10 (1980) 63-82]. Using a coding tree and its concomitant tables, a systematical way can help us to investigate the structural representation of t-ary trees. Consequently, we develop efficient algorithms for determining the rank of a given t-ary tree in lexicographic order (i.e., a ranking algorithm), and for converting a positive integer to its corresponding RD-sequence (i.e., an unranking algorithm). Both the ranking and unranking algorithms can be run in O(tn) time and without computing all the entries of the coefficient table.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E94.D.226/_p
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@ARTICLE{e94-d_2_226,
author={Ro-Yu WU, Jou-Ming CHANG, Yue-Li WANG, },
journal={IEICE TRANSACTIONS on Information},
title={Ranking and Unranking of t-Ary Trees Using RD-Sequences},
year={2011},
volume={E94-D},
number={2},
pages={226-232},
abstract={In this paper, we introduce a concise representation, called right-distance sequences (or RD-sequences for short), to describe all t-ary trees with n internal nodes. A result reveals that there exists a close relationship between the representation and the well-formed sequences suggested by Zaks [Lexicographic generation of ordered trees, Theoretical Computer Science 10 (1980) 63-82]. Using a coding tree and its concomitant tables, a systematical way can help us to investigate the structural representation of t-ary trees. Consequently, we develop efficient algorithms for determining the rank of a given t-ary tree in lexicographic order (i.e., a ranking algorithm), and for converting a positive integer to its corresponding RD-sequence (i.e., an unranking algorithm). Both the ranking and unranking algorithms can be run in O(tn) time and without computing all the entries of the coefficient table.},
keywords={},
doi={10.1587/transinf.E94.D.226},
ISSN={1745-1361},
month={February},}
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TY - JOUR
TI - Ranking and Unranking of t-Ary Trees Using RD-Sequences
T2 - IEICE TRANSACTIONS on Information
SP - 226
EP - 232
AU - Ro-Yu WU
AU - Jou-Ming CHANG
AU - Yue-Li WANG
PY - 2011
DO - 10.1587/transinf.E94.D.226
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E94-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2011
AB - In this paper, we introduce a concise representation, called right-distance sequences (or RD-sequences for short), to describe all t-ary trees with n internal nodes. A result reveals that there exists a close relationship between the representation and the well-formed sequences suggested by Zaks [Lexicographic generation of ordered trees, Theoretical Computer Science 10 (1980) 63-82]. Using a coding tree and its concomitant tables, a systematical way can help us to investigate the structural representation of t-ary trees. Consequently, we develop efficient algorithms for determining the rank of a given t-ary tree in lexicographic order (i.e., a ranking algorithm), and for converting a positive integer to its corresponding RD-sequence (i.e., an unranking algorithm). Both the ranking and unranking algorithms can be run in O(tn) time and without computing all the entries of the coefficient table.
ER -
English
