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A guided tour to approximate string matching

ACM Computing SurveysVolume 33Issue 1March 2001 pp 31–88https://doi.org/10.1145/375360.375365
Online:01 March 2001Publication History
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Abstract

We survey the current techniques to cope with the problem of string matching that allows errors. This is becoming a more and more relevant issue for many fast growing areas such as information retrieval and computational biology. We focus on online searching and mostly on edit distance, explaining the problem and its relevance, its statistical behavior, its history and current developments, and the central ideas of the algorithms and their complexities. We present a number of experiments to compare the performance of the different algorithms and show which are the best choices. We conclude with some directions for future work and open problems.

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Reviews

Paul Cull

String matching is used in a variety of areas, including word processing, information retrieval, and computational biology. This survey considers the problem of locating within a text string all substrings which are nearly the same as an input pattern string. Distance between strings is measured by the edit distance or one of its variants. No preprocessing of the text, like building an index, is allowed. These restrictions may not be appropriate in all applications. For example, in some biological applications movement of gene segments may make edit distance an inappropriate measure of distance between strings. Also, in many information retrieval applications, indices are created, making the no preprocessing assumption false. In spite of these limitations, this is still an important and useful survey. The simplest approach to finding all occurrences of a pattern of length p within a text of length t is to compare the pattern with each run of p characters within the text. This will take time O(pt). If one wants to allow for a fixed number of errors, say k, independent of the lengths of the pattern and text then O(kpt) time will suffice. Can this obvious approach be improved__?__ This has been an active research area for the last twenty years, and this survey outlines the improvements that have been made. As is often the case in algorithms, there may be a difference between theoretically and practically good algorithms. For example, a theoretical algorithm may only be faster for impractically large problems, or a fast algorithm may use impractical amounts of space. So, very reasonably this survey not only discusses the theoretical advances, but also comments on the practicality of the various algorithms. The now classical algorithm for approximate string matching is a dynamic programming algorithm. This survey points out how improvements have been made by computing the dynamic programming matrix in various orders, by avoiding calculating unneeded parts of the matrix, and by trading space for time in these calculations. The survey also describes algorithms which are based on finite automata. In practice, both types of algorithms can be improved by using the inherent parallelism of the word level over the bit or character level. The author also describes filtering algorithms which will eliminate parts of the text where there cannot be approximate matches. In a second phase, the non-eliminated portions have to be checked to see if they really are approximate matches. A most interesting feature of this survey is the inclusion of some experimental comparisons of several of the discussed algorithms. The experiments compare the algorithms on data from various application areas. Not unexpectedly there is no clear winner. The behavior of the algorithms depends on the statistics of the input data. The author has available on his Web site a hybrid program which does string matching by heuristically choosing one of the three algorithms that his experiments show are good on various sorts of data. Overall, this is a thorough review of one area of string matching. There are about 150 references, of which about 15 are by this survey's author. The article is written in an easy to read, non-formal style. There are no theorem/proofs, instead there are a few short proofs and a number of heuristic arguments. There are a few lapses in English and a couple of typos, but these are minor and do not interfere with the readability. This survey should be required reading for those interested in approximate string matching.

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