Introduction of suffix tree

Aug 21, 20123 likes2,570 views

This document discusses suffix trees, including their definition, important contributors, construction, implementation, and applications. Key points: - A suffix tree is a compressed trie representing all suffixes of a string. It allows efficient pattern matching in linear time. - Important contributors include Weiner (1973), McCreight (1976), Ukkonen (1995), and Farach (1997) who developed faster construction algorithms. - There are multiple ways to implement a suffix tree, including using sibling lists, hash maps, balanced search trees, or sorted arrays. External memory may be needed for very large trees. - Applications include fast substring search, longest common substring problems, and data compression. References provide more details on

? Abstract
? Construction
? Implementation
? Reference

? 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

? 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

? String S = {peeper$}; Suffix(S,0) = {peeper$}
ROOT
p

e

e

p

e

r
peeper

$

? String S = {peeper$}; Suffix(S,1) = {eeper$}
ROOT
p e

e e

e p

p e

e r
eeper
r
peeper $

$

? 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 $

$

? 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 $

$

? 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 $

$

? 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 $

$

? 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 $

$

? 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 $

$

? The suffix tree of {peeper$} is completed.
ROOT
r
pe e
r
eper r eper per r
peeper per eeper eper er $

$ $ $ $
$

? 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

Lookup Insertion Traversal
Sibling lists /
unsorted arrays
Hash maps
Balanced search
tree
Sorted arrays
Hash maps +
sibling lists

? How to implement the suffix tree/trie �C child && sibling
ROOT

-85 0 72

0 0 -85 72

0 72 -85 0

-85 0 72

0 72

72

$? struct node{ struct node *child, *sibling; int c_num, s_num; int slope; int node_type; char *obslist_file; } ? node_type is used to indicate what the node is. (root / inter-node / leaf / terminal) ? obslist_file is used for external memory. The data that seldom queried will be recorded in this file.$

? 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.

? Wikipedia �C 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

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Dev Dives: Unleash the power of macOS Automation with UiPathUiPathCommunity

Join us on March 27 to be among the first to explore UiPath innovative macOS automation capabilities. This is a must-attend session for developers eager to unlock the full potential of automation. ? This webinar will offer insights on: How to design, debug, and run automations directly on your Mac using UiPath Studio Web and UiPath Assistant for Mac. We��ll walk you through local debugging on macOS, working with native UI elements, and integrating with key tools like Excel on Mac. This is a must-attend session for developers eager to unlock the full potential of automation. ??? Speakers: Andrei Oros, Product Management Director @UiPath SIlviu Tanasie, Senior Product Manager @UiPath