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Paper Abstract and Keywords
Presentation 2006-09-26 15:40
A New Representation of Ordered Trees
Jesper Jansson, Kunihiko Sadakane (Kyushu Univ.), Wing-Kin Sung (NUS)
Abstract (in Japanese) (See Japanese page) 
(in English) There exist two well-known succinct representations of ordered trees:
BP (balanced parenthesis) [Munro, Raman 2001] and DFUDS (depth first
unary degree sequence) [Benoit et al. 2005].
Both have size $2n+\order(n)$ bits for $n$-node trees, which matches
the information-theoretic lower bound.
Many fundamental operations on trees
can be done in constant time on word RAM, for example finding parent,
the first child, next sibling, the number of descendants, etc.
However there has been no single representation supporting every existing
operation in constant time; BP does not support $i$-th child,
while DFUDS does not support {\lca} (lowest common ancestor).

In this paper, we give the first succinct tree representation supporting
every one of the fundamental operations previously proposed for BP or DFUDS
along with some new operations in constant time.
Moreover, its size surpasses the
information-theoretic lower bound and matches the entropy
of the tree based on the distribution of node degrees.
We call this an ultra-succinct data structure.
As a consequence, a tree in which every internal node has exactly two children
can be represented in $n+\order(n)$ bits.
Keyword (in Japanese) (See Japanese page) 
(in English) succinct data structures / entropy / ordered trees / / / / /  
Reference Info. IEICE Tech. Rep., vol. 106, no. 258, COMP2006-29, pp. 31-37, Sept. 2006.
Paper # COMP2006-29 
Date of Issue 2006-09-19 (COMP) 
ISSN Print edition: ISSN 0913-5685  Online edition: ISSN 2432-6380
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Conference Information
Committee COMP  
Conference Date 2006-09-26 - 2006-09-26 
Place (in Japanese) (See Japanese page) 
Place (in English) JAIST 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2006-09-COMP 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) A New Representation of Ordered Trees 
Sub Title (in English)  
Keyword(1) succinct data structures  
Keyword(2) entropy  
Keyword(3) ordered trees  
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1st Author's Name Jesper Jansson  
1st Author's Affiliation Kyushu University (Kyushu Univ.)
2nd Author's Name Kunihiko Sadakane  
2nd Author's Affiliation Kyushu University (Kyushu Univ.)
3rd Author's Name Wing-Kin Sung  
3rd Author's Affiliation National University of Singapore (NUS)
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Speaker
Date Time 2006-09-26 15:40:00 
Presentation Time 35 
Registration for COMP 
Paper # IEICE-COMP2006-29 
Volume (vol) IEICE-106 
Number (no) no.258 
Page pp.31-37 
#Pages IEICE-7 
Date of Issue IEICE-COMP-2006-09-19 


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