String Matching

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String Matching

• Thomas Berry
• Room 706A

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Last Week

• An efficient algorithm has a polynomial worst
  case time complexity. Which means that they are
  all of the form O(nk). Where k is an integer
  greater than 0. For example O(n), O(n2), etc..
• String matching is the searching for a pattern P
  of length m in a text T of length n. Where ngtm.

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This Week

• Show the Horspool algorithm
• Show Berry Ravindran

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Theoretical evaluation

• KMP has a time complexity of O(nm).
• The following all have time complexities of
  O(nm)
• Brute Force,Horspool and the Berry Ravindran.
• So theoretically the KMP is the best algorithm
  for string matching. Is this true in practice?

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Horspool Algorithm

• Performs comparisons from right to left.
• Uses one shift table to calculate the shift after
  a full match or mismatch.
• Shift table calculates the position of the
  mismatched text character in the pattern. If the
  character is not in the pattern then we shift by
  m positions.

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Horspool Algorithm

• How do we construct the table?
• The table is constructed by numbering the
  characters of the pattern from left to right
  starting with m-1.
• If a character repeats then the lower value is
  used.
• Example with ababcab from the KMP example.

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Horspool Example
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Horspool Shift Table
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Horspool Example
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Horspool Shift Table
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Horspool Example
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Horspool Example
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Horspool Example
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Horspool Example
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Horspool Review

• Horspool takes less comparisons than the KMP and
  Brute Force algorithms.
• This is due to the larger shift when the
  algorithm mismatches.

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Berry Ravindran

• My own algorithm. Very simplistic?
• Searches right to left as the Horspool.
• Uses one shift table.
• Shifts on the two characters after the
  text/pattern alignment.
• Over 2 million trials with English text was the
  most efficient algorithm by 30

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Berry Ravindran algorithm
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B R Example
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B R Example
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B R Example no. 2
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B R Example no. 2
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B R Example no. 2
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B R Example no. 2
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B R Example no. 2
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Conclusion

• Although the theoretical evaluation claims that
  the KMP is the best algorithm for the task of
  string matching. We can see that others are
  better in practice and that the KMP is one of the
  worst in practice for searching in English text.
  This is due to us using a text and pattern that
  are not the worst case.

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Conclusion

• The theoretical evaluation gives an idea of the
  efficiency of the algorithm. But not until we
  have tested it in practice can we be sure of our
  claims.