STRING MATCHING

Exact String Matching

Algorithm And Analysis BCS-4

COMSATS Institute Of Information Technology, wah

Ehtisham Arshad (FA11-BsCS-059) Hissam Yousaf (Sp12-BsCS-036)

Group Members

Exact String Matching AlgorithmsKnuth Morris And Pratt – KMPBoyer Moore - BM

Group Project

The goal of any string-searching algorithm is to determine whether or not a match of a particular string exists within another (typically much longer) string.

Many such algorithms exist, with varying efficiencies.

• Knuth Morris And Pratt - KMP• Boyer Moore - BM

Problem

IntroductionThe algorithm was conceived in 1974 by Donald Knuth and Vaughan Pratt, and independently by James H. Morris. The three published it jointly in 1977

Knuth Morris and Pratt

KMP, linear time algorithm for the string matching problem, every character is checked.

Introduction Developed in 1977, the BM string search

algorithm is a particularly efficient algorithm.

Boyer Moore

This algorithm’s execution time can be sub-linear, as not every character of the string to be searched needs to be checked.

Knuth Morris and Pratt Implementation

Left to Right CheckScans the string from left to right to match a particular given pattern

If a match is found at the first index, the next index is checked otherwise the pointer moves to right of the string

Character Skip using KMP tablePartial_lenght – 1 (for Initial Match)Partial_lenght – index value = SKIP

Knuth Morris and Pratt

Step 1:compare p[1] with S[1]

Sp

Step 2: compare p[2] with S[2]

Implementation of KMP

a b c a b a a b c a b a c

a b a a


a b a a

Step 3: compare p[3] with S[3]

S

P


a b a a


Mismatch occurs here..

Since mismatch is detected, shift ‘p’ one position to the left and perform steps analogous to those from step 1 to step 3.


a b a a

Finally, a match would be found after shifting ‘p’ three times to the right side.

S

P

Final Step:


Boyer Moore Implementation

Bad Character RuleOccurs when rightmost character of the pattern doesn’t match with the given string’s index.

Shifting Rules in BM

Good Suffix RuleIf a number of characters match with the given string then the good suffix shift occurs.

Step 1: Try to match first m characters

Pattern: STING

String: A STRING SEARCHING EXAMPLE CONSISTING OF TEXT

Implementation of BM

This fails. Slide pattern right to look for other matches.Since R isn’t in the pattern, slide down next to R.

Step 2:Pattern : STING String : A STRING SEARCHING EXAMPLE CONSISTING OF TEXT


Fails again. Rightmost character S is in pattern precisely once, so slide until two S's line up.

String : A STRING SEARCHING EXAMPLE CONSISTING OF TEXT

No C in pattern. Slide past it.

Final Step:

Pattern : STING String : A STRING SEARCHING EXAMPLE CONSISTING OF TEXT


Match found..

Pattern(Length)

1st Time(ms)

2nd Time(ms)

3rd Time(ms)

4th Time(ms)

5th Time(ms)

Hi(2) 8ms 9ms 6ms 10ms 9ms

Pakistan(8) 20ms 19ms 22ms 20ms 21ms

Longest(30)

38ms 46ms 39ms 37ms 43ms

Run Time for KMP

The Table shows that the KMP has a best case for Short Strings and patterns.The Worst Case scenario are Larger Strings or Patterns.

Avg Time for shortest (2) = 8.4ms Avg Time for Intermediate = 20.4msAvg Time for Longest = 40.6ms

Pattern (Length)

1st Timems

2nd Timems

3rd Timems

4th Timems

5th Timems

Hi(2) 378ms 512ms 555ms 445ms 380ms

Pakistan(8) 27ms 25ms 24ms 29ms 35ms

Longest(30)

17ms 16ms 17ms 18ms 11ms

Run Time for Boyer Moore

Avg Time for shortest (2) = 454ms Avg Time for Intermediate = 20msAvg Time for Longest = 15.7ms

The Table shows that the BM has a best case for Larger Strings and patterns.The Worst Case scenario is short Strings or Patterns.

Graph Comparison

P

roce

ssin

g t

ime (

ms)

On average, for sufficiently large alphabets (8 characters) Boyer- Moore has fast running time and sub-linear number of character comparisons.

On average, and in worst cases Boyer-Moore is faster than “Boyer-Moore-like” algorithms.

The running time of Knuth-Morris-Pratt algorithm is proportional to the time needed to read the characters in text and pattern. In other words, the worst-case running time of the algorithm is O(m + n) and it requires O(m) extra space.

Time Complexity of KMP

• Boyer requires a preprocessing time of O(m+∂)

• The running time of BM algorithm is O(mn)

•

Time Complexity of BM

• The Boyer Moore Algorithm performs best for O(n/m)

• Worst Case of BM is 3n.

KMP and Boyer Moore finds its applications in many core Digital Systems and processes e.g.

Applications of KMP and BM

Digital libraries Screen scrapers Word processors Web search engines Spam filters Natural language processing

Thank you

Exact String Matching

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STRING MATCHING