Approximate string search is the name that is used for a category of techniques for finding strings that approximately match some given pattern string. It may also be known as approximate or inexact matching.
Approximate string searching has two different flavors:
- finding one or more matching substrings of a text, and
- finding similar strings in a string set, often referred to as a dictionary.
Approximate string searching has many application areas including information retrieval, spellchecking and computational biology [1].
Similarity functions
The cornerstone of any approximate searching method is a similarity function or string metric. Among the most commonly used similarity functions are Levenshtein distance (a type of edit distance) and n-gram distance. The latter is based on counting the number of common n-grams, and is used mostly for filtering. In contrast to n-gram distance, Levenshtein distance is a de-facto standard similarity function. It has several extensions. One well known extension is Damerau-Levenshtein distance that counts transposition as a single edit operation. Another extension is the so-called generalized or weighted Levenshtein distance. It assigns different costs to elementary edit operations. Ukkonen [2] described even more sophisticated similarity function where edit operations go beyond single-character insertions, deletions and substitutions and include substitutions of arbitrary-length strings.
On-line vs. off-line
Traditionally, approximate string matching algorithms are classified into two categories: on-line and off-line. With on-line algorithms the pattern can be preprocessed before searching but the text cannot. In other words, on-line techniques do searching without indexation. Early algorithms for on-line approximate matching were suggested by Wagner and Fisher[3] and by Sellers. [4] Both algorithms are based on dynamic programming but solve different problems. Sellers' algorithm searches approximately for a substring in a text while the algorithm of Wagner and Fisher calculates Levenshtein distance, being appropriate for dictionary fuzzy search only.
On-line searching techniques were repeatedly improved. Perhaps the most famous improvement is the bitap algorithm (also known as the shift-or and shift-and algorithm), which is very efficient for relatively short pattern strings. The Bitap algorithm is the heart of the Unix searching utility agrep. An excellent review of on-line searching algorithms was done by G. Navarro.[5]
Although very fast on-line techniques exist, their performance on large data is unacceptable. Text preprocessing or indexing makes searching dramatically faster. Today, a variety of indexing algorithms are presented. Among them are suffix trees[6], metric trees[7] and n-gram methods.[8][9] For a detailed list of indexing techniques see the paper of Navarro et al.[10]
See also
References
- ^ R. Baeza-Yates and G. Navarro. A faster algorithm for approximate string matching. In Dan Hirchsberg and Gene Myers, editors, Combinatorial Pattern Matching (CPM'96), LNCS 1075, pages 1--23, Irvine, CA, Jun 1996.
- ^ D. Gusfield. Algorithms on strings, trees, and sequences: computer science and computational biology. Cambridge University Press, New York, NY, USA, 1997.
- ^ R. Baeza-Yates and G. Navarro. Fast Approximate String Matching in a Dictionary.Proc. SPIRE'98. IEEE CS Press, pages 14-22.
- ^ G. Myers. A fast bit-vector algorithm for approximate string matching based on dynamic programming, Journal of the ACM (JACM) 46 (3), May 1999, 395 - 415.
- ^ G. Navarro. A guided tour to approximate string matching. ACM Computing Surveys (CSUR) archive 33(1), pp 31-88, 2001.
- ^ G. Navarro, Ricardo Baeza-Yates, E. Sutinen and J. Tarhio. Indexing Methods for Approximate String Matching.IEEE Data Engineering Bulletin 24(4):19-27, 2001.
- ^ P.H. Sellers. The Theory and Computation of Evolutionary Distances: Pattern Recognition. Journal of Algorithms, 1:359-373, 1980.
- ^ E. Ukkonen, Algorithms for approximate string matching. Information and Control 64, 100-118. 1985.
- ^ R. Wagner and M. Fischer, The string-to-string correction problem, Journal of the association for computing machinery, vol. 21, pp. 168 173, 1974.
- ^ J. Zobel, P. Dart. Finding approximate matches in large lexicons. Software-Practice & Experience 25(3), pp 331-345, 1995.
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