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Fuzzy String Searching




finding strings that approximately match some given pattern string.
Fuzzy 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
dictionary. Fuzzy string searching has many application areas including
information retrieval, spellchecking and computational biology .

The corner stone of any approximate searching method is a '''similarity function.
Among most commonly used similarity functions are Levenshtein Distance and N-gram Distance .
The latter is based on counting of the number of common N-gram s.
It 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 described even more sophisticated similarity function
where edit operations go beyond single-character insertions, deletions and substitutions
and include substitutions of arbitrary-length strings.

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 and by Sellers . 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 Bitap Algorithm (also known as shift-or and shift-and algorithm),
which is very efficient
for relatively short pattern strings. Bitap Algorithm is the heart of
Unix searching Utility Agrep . An excellent review of
on-line searching algorithms was done by G. Navarro .

Although very fast on-line techniques exist their
performance on large data is unacceptable.
In its turn, text preprocessing, or in other words indexing, makes searching dramatically faster.
Today, a variety of indexing algorithms are presented. Among them are Suffix Trees ,
Metric Trees and N-gram methods .
For a detailed list of indexing techniques I would address the reader to the paper of Navarro et. al.


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