| 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 |
| Download PDF |
|
| 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) |
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| 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 |
| Keyword(4) |
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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 |
Author-2 |
| Date Time |
2006-09-26 15:40:00 |
| Presentation Time |
35 minutes |
| Registration for |
COMP |
| Paper # |
COMP2006-29 |
| Volume (vol) |
vol.106 |
| Number (no) |
no.258 |
| Page |
pp.31-37 |
| #Pages |
7 |
| Date of Issue |
2006-09-19 (COMP) |
|