2. Abstract
Construction
Implementation
Reference
3. Alias: position tree, PAT tree
Important people
o Weiner (1973) first introduction
o McCreight (1976) simplified the construction
o Ukkonen (1995) fastest construction algorithm
o Farach (1997) optimal construction algorithm for all alphabets
4. Trie
string: S, length: N
Suffix tree of S:
o the paths from the root to the leaves have a one-to-one relationship
with the suffixes of S.
o edges spell non-empty strings.
o all internal nodes (except perhaps the root) have at least two
children
-- reference. Wikipedia. Suffix tree
5. String S = {peeper$}; Suffix(S,0) = {peeper$}
ROOT
p
e
e
p
e
r
peeper
$
6. String S = {peeper$}; Suffix(S,1) = {eeper$}
ROOT
p e
e e
e p
p e
e r
eeper
r
peeper $
$
7. String S = {peeper$}; Suffix(S,2) = {eper$}
ROOT
p e
e e p
e p e
p e r
eper
e r
eeper $
r
peeper $
$
8. String S = {peeper$}; Suffix(S,3) = {per$}
ROOT
p e
e e p
e r p e
per
p e r
$ eper
e r
eeper $
r
peeper $
$
9. String S = {peeper$}; Suffix(S,4) = {er$}
ROOT
p e
e e p r
er
e r p e
per $
p e r
$ eper
e r
eeper $
r
peeper $
$
10. String S = {peeper$}; Suffix(S,5) = {r$}
ROOT
r
p e
r
e e p r
er $
e r p e
per $
p e r
$ eper
e r
eeper $
r
peeper $
$
11. However, this isn’t a suffix tree. It’s a suffix trie.
ROOT
r
p e
r
e e p r
er $
e r p e
per $
p e r
$ eper
e r
eeper $
r
peeper $
$
12. Suffix trie can be compressed to suffix tree.
ROOT
r
p e
r
e e p r
er $
e r p e
per $
p e r
$ eper
e r
eeper $
r
peeper $
$
13. The suffix tree of {peeper$} is completed.
ROOT
r
pe e
r
eper r eper per r
peeper per eeper eper er $
$ $ $ $
$
14. There are many ways to implement suffix tree.
o Sibling lists / unsorted arrays
o Hash maps
o Balanced search tree
o Sorted array
o Hash maps + sibling lists
16. How to implement the suffix tree/trie – child && sibling
ROOT
-85 0 72
0 0 -85 72
0 72 -85 0
-85 0 72
0 72
72
17. struct node{
struct node *child, *sibling;
int c_num, s_num;
int slope;
int node_type;
char *obslist_file;
}
node_type is used to indicate what the node is.
(root / inter-node / leaf / terminal)
obslist_file is used for external memory.
The data that seldom queried will be recorded in this file.
18. If the trie is too big, how can I do?
o If trie is constructed by C-S-Link, every subtree is a binary tree.
o Record the in-order and pre-/post- order sequence.
o Use two sequence to reconstruct, if we want to query the subtree.
19. Wikipedia – suffix tree
http://en.wikipedia.org/wiki/Suffix_tree
Data Structures, Algorithms, & Applications in Java Suffix Trees
Copyright 1999 Sartaj Sahni
http://www.cise.ufl.edu/~sahni/dsaaj/enrich/c16/suffix.htm#tree
Websites for suffix tree/trie
o http://blog.csdn.net/ljsspace/article/details/6581850
o http://www.allisons.org/ll/AlgDS/Tree/Suffix/
o http://blog.csdn.net/TsengYuen/article/details/4815921
o http://www.cppblog.com/yuyang7/archive/2009/03/29/78252.html
