String Matching with Variable Length Gaps By Philip Bille, Inge Li - PowerPoint PPT Presentation

String Matching with Variable Length Gaps By Philip Bille, Inge Li Gørtz, Hjalte Wedel Vildhøj and David Kofoed Wind Presented by Hjalte Wedel Vildhøj October 13, 2010 SPIRE 2010, Los Cabos, Mexico

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Find the end positions for all occurrences of P in T .

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T .

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT �� Solution:

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT 6 6 T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT end pos in T � � Solution: 17

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT 8 6 T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT � � Solution: 17 Not a valid match!

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT 6 6 T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT end pos in T � � Solution: 17 , 28

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT 5 7 T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT end pos in T � � Solution: 17 , 28

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT 3 7 T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT end pos in T � � Solution: 17 , 28 , 31

The Variable Length Gap Problem Given some string T ∈ Σ + and a variable length gap pattern P = P 1 · g { a 1 , b 1 } · P 2 · g { a 2 , b 2 } · · · g { a k − 1 , b k − 1 } · P k . Some x ∈ Σ ∗ s.t. a 1 ≤ | x | ≤ b 1 Find the end positions for all occurrences of P in T . Example: P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT T = ATCGGCTCCAGACCAGTACCCGTTCCGTGGT � � Solution: 17 , 28 , 31

A Closer Look At The Problem P 3 P 3 P 3 P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT P 3 P 2 P 2 P 2 P 2 P 2 P 1 P 1 P 1 P 1 P 1 A T C G G C T C C A G A C C A G T A C C C G T T C C G T G G T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A Closer Look At The Problem Parameters n = | T | α = # occ. of P 1 , P 2 , . . . , P k in T k k � � m = | P i | A = a i i = 1 i = 1 P 3 P 3 P 3 P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT P 3 P 2 P 2 P 2 P 2 P 2 P 1 P 1 P 1 P 1 P 1 A T C G G C T C C A G A C C A G T A C C C G T T C C G T G G T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A Closer Look At The Problem Parameters n = | T | α = # occ. of P 1 , P 2 , . . . , P k in T k k � � m = | P i | A = a i i = 1 i = 1 Known Upper Bounds By Time Space � � n ( k log w Bille & Thorup 1 O + log k ) + m log m + A O ( m + A ) w Morgante et al. 2 O (( n + m ) log k + α ) O ( m + α ) 1 P. Bille and M. Thorup. Regular expression matching with multi-strings and intervals. In Proc. 21st SODA, 2010 2 M. Morgante, A. Policriti, N. Vitacolonna, and A. Zuccolo. Structured motifs search. J. Comput. Bio. , 12(8):1065-1082, 2005

A Closer Look At The Problem Parameters n = | T | α = # occ. of P 1 , P 2 , . . . , P k in T k k � � m = | P i | A = a i i = 1 i = 1 Known Upper Bounds By Time Space � � n ( k log w Bille & Thorup O + log k ) + m log m + A O ( m + A ) w Morgante et al. O (( n + m ) log k + α ) O ( m + α ) Can you get the best of both?

Illustrating the Algorithm P 3 P 3 P 3 P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT P 3 P 2 P 2 P 2 P 2 P 2 P 1 P 1 P 1 P 1 P 1 A T C G G C T C C A G A C C A G T A C C C G T T C C G T G G T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 L 2 L 3

Illustrating the Algorithm P 3 P 3 P 3 P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT P 3 P 2 P 2 P 2 P 2 P 2 P 1 P 1 P 1 P 1 P 1 A T C G G C T C C A G A C C A G T A C C C G T T C C G T G G T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 dead L 2 L 3

Illustrating the Algorithm P 3 P 3 P 3 P = A · g { 6 , 7 } · CC · g { 2 , 6 } · GT P 3 P 2 P 2 P 2 P 2 P 2 P 1 P 1 P 1 P 1 P 1 A T C G G C T C C A G A C C A G T A C C C G T T C C G T G G T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 L 2 L 3

String Matching with Variable Length Gaps By Philip Bille, Inge Li - PowerPoint PPT Presentation

String Matching with Variable Length Gaps By Philip Bille, Inge Li Grtz, Hjalte Wedel Vildhj and David Kofoed Wind Presented by Hjalte Wedel Vildhj October 13, 2010 SPIRE 2010, Los Cabos, Mexico The Variable Length Gap Problem Given some

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String Matching with Variable Length Gaps By Philip Bille, Inge Li - PowerPoint PPT Presentation

String Matching with Variable Length Gaps By Philip Bille, Inge Li Grtz, Hjalte Wedel Vildhj and David Kofoed Wind Presented by Hjalte Wedel Vildhj October 13, 2010 SPIRE 2010, Los Cabos, Mexico The Variable Length Gap Problem Given some

Basic SQL types String Char(n): fixed length. Padded Varchar(n): variable length

String Matching Inge Li Grtz CLRS 32 String Matching String matching problem: string

String Matching String matching problem: string T (text) and string P (pattern) over an

CS 1501 www.cs.pitt.edu/~nlf4/cs1501/ String Pattern Matching General idea Have a pattern

Scalable String Matching on the Scalable String Matching on the Scalable String Matching on the

String Edit Distance Matching Problem with Moves Graham Cormode, S. Muthukrishnan

VGRAM: Improving Performance of Approximate Queries on String Collections Using Variable-Length

String Matching II Algorithm : Design &amp; Analysis [19] In the last class Simple String

String Matching Algorithm : Design &amp; Analysis [18] In the last class Optimal Binary

Chapter 32: String Matching Fall 2007 Simonas altenis simas@cs.aau.dk Modified by Pierre

String Matching with Involutions Florin Manea Challenges in Combinatorics on Words April 2013

String Matching: Boyer-Moore Algorithm Greg Plaxton Theory in Programming Practice, Fall 2005

Lecture 8 n Agenda: n String matching n How to evaluate a pattern recognition system String

String matching Announcements Programming assignment 1 posted - need to submit a .sh file The

String Matching: Rabin-Karp Algorithm Greg Plaxton Theory in Programming Practice, Fall 2005

Sequence to Sequence Video to Text Venugopalan et al. Given a variable-length sequence of

Tries and Suffix Trees Inge Li Grtz String indexing problem String matching problem. Given

Stochastic chains with memory of variable length Antonio Galves Universidade de So Paulo AofA

! The variable-length code is a prefix min f ( c ) d ( c ) code : no binary string is

Regular Expressions Simple matching and searching String: My name is Claus Regex: My name is

CSE182-L7 Dicitionary matching Pattern matching October 09 CSE182 Dictionary Matching

Matching the circular Wilson loop with dual open string solution at 1 -loop in strong coupling M.

Counting Permutations &amp; Combinations Strings Given an alphabet (a finite set) B, we can

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