Average case analysis for tree labelling schemes

Ming-Yang Kao*, Xiang Yang Li, Weizhao Wang

*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We study how to label the vertices of a tree in such a way that we can decide the distance of two vertices in the tree given only their labels. For trees, Gavoille et al. [7] proved that for any such distance labelling scheme, the maximum label length is at least 1/8 log2 n - O(log n) bits. They also gave a separator-based labelling scheme that has the optimal label length Θ(log n · log(Hn(T))), where Hn(T) is the height of the tree. In this paper, we present two new distance labelling schemes that not only achieve the optimal label length Θ (log n · log(Hn(T))), but also have a much smaller expected label length under certain tree distributions. With these new schemes, we also can efficiently find the least common ancestor of any two vertices based on their labels only.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings
Pages136-145
Number of pages10
DOIs
StatePublished - Dec 1 2005
Event16th International Symposium on Algorithms and Computation, ISAAC 2005 - Hainan, China
Duration: Dec 19 2005Dec 21 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3827 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other16th International Symposium on Algorithms and Computation, ISAAC 2005
CountryChina
CityHainan
Period12/19/0512/21/05

Fingerprint

Average-case Analysis
Labeling Scheme
Labeling
Labels
Separator
Separators

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kao, M-Y., Li, X. Y., & Wang, W. (2005). Average case analysis for tree labelling schemes. In Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings (pp. 136-145). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS). https://doi.org/10.1007/11602613_15
Kao, Ming-Yang ; Li, Xiang Yang ; Wang, Weizhao. / Average case analysis for tree labelling schemes. Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. 2005. pp. 136-145 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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author = "Ming-Yang Kao and Li, {Xiang Yang} and Weizhao Wang",
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Kao, M-Y, Li, XY & Wang, W 2005, Average case analysis for tree labelling schemes. in Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3827 LNCS, pp. 136-145, 16th International Symposium on Algorithms and Computation, ISAAC 2005, Hainan, China, 12/19/05. https://doi.org/10.1007/11602613_15

Average case analysis for tree labelling schemes. / Kao, Ming-Yang; Li, Xiang Yang; Wang, Weizhao.

Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. 2005. p. 136-145 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3827 LNCS).

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

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Kao M-Y, Li XY, Wang W. Average case analysis for tree labelling schemes. In Algorithms and Computation - 16th International Symposium, ISAAC 2005, Proceedings. 2005. p. 136-145. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/11602613_15