31:
868:
and off-line. With on-line algorithms the pattern can be processed before searching but the text cannot. In other words, on-line techniques do searching without an index. Early algorithms for on-line approximate matching were suggested by Wagner and
Fischer and by Sellers. Both algorithms are based
249:
Other matchers specify the number of operations of each type separately, while still others set a total cost but allow different weights to be assigned to different operations. Some matchers permit separate assignments of limits and weights to individual groups in the pattern.
209:
Different approximate matchers impose different constraints. Some matchers use a single global unweighted cost, that is, the total number of primitive operations necessary to convert the match to the pattern. For example, if the pattern is
460:
A brute-force approach would be to compute the edit distance to P for all substrings of T, and then choose the substring with the minimum distance. However, this algorithm would have the running time
443:
374:
318:
844:) time with the dynamic programming algorithm cannot work within a limited time. So, the idea is to reduce the number of candidate pairs, instead of computing the similarity of
564:
125:
These three operations may be generalized as forms of substitution by adding a NULL character (here symbolized by *) wherever a character has been deleted or inserted:
918:
A computational survey of dictionary methods (i.e., methods that permit finding all dictionary words that approximately match a search pattern) is given by
Boytsov.
526:
70:
The closeness of a match is measured in terms of the number of primitive operations necessary to convert the string into an exact match. This number is called the
1874:
884:(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
1769:
873:
but solve different problems. Sellers' algorithm searches approximately for a substring in a text while the algorithm of Wagner and
Fischer calculates
1808:
1734:
1739:
58:
approximately (rather than exactly). The problem of approximate string matching is typically divided into two sub-problems: finding approximate
1744:
1503:
1382:
1279:
1260:
856:
and other greedy and approximation algorithms. Most of them are designed to fit some framework (such as Map-Reduce) to compute concurrently.
692:), the only difference being that we must initialize the first row with zeros, and save the path of computation, that is, whether we used
1986:
1729:
1955:
1475:
Baeza-Yates, R.; Navarro, G. (June 1996). "A faster algorithm for approximate string matching". In Dan
Hirchsberg; Gene Myers (eds.).
1823:
1764:
1636:
1671:
1588:
914:
methods. A detailed survey of indexing techniques that allows one to find an arbitrary substring in a text is given by
Navarro
1851:
991:
945:
String matching cannot be used for most binary data, such as images and music. They require different algorithms, such as
1856:
1711:
1007:
1996:
1935:
1785:
898:
Although very fast on-line techniques exist, their performance on large data is unacceptable. Text preprocessing or
1940:
1818:
1721:
1598:
981:
849:
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971:
1991:
1950:
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makes searching dramatically faster. Today, a variety of indexing algorithms have been presented. Among them are
1749:
379:
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1681:
323:
1894:
258:
One possible definition of the approximate string matching problem is the following: Given a pattern string
1480:
1436:
1298:
769:), and follow the path of computation backwards, back to the row number 0. If the field we arrived at was
261:
834:
Another recent idea is the similarity join. When matching database relates to a large scale of data, the
1899:
1841:
1701:
1629:
899:
880:
On-line searching techniques have been repeatedly improved. Perhaps the most famous improvement is the
1348:
Sellers, Peter H. (1980). "The Theory and
Computation of Evolutionary Distances: Pattern Recognition".
1219:
Boytsov, Leonid (2011). "Indexing methods for approximate dictionary searching: Comparative analysis".
1706:
1173:
996:
976:
946:
874:
677:
230:
by two substitutions. If all operations count as a single unit of cost and the limit is set to one,
30:
1904:
1485:
1441:
1303:
1001:
870:
478:
62:
matches inside a given string and finding dictionary strings that match the pattern approximately.
1833:
1800:
1537:
1514:
1454:
1415:
1316:
1236:
51:
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is often used to integrate approximate string searching into various command-line applications.
188:, in which the positions of two letters in the string are swapped, to be a primitive operation.
1965:
1499:
1378:
1275:
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676:) is very similar to computing the edit distance between two strings. In fact, we can use the
531:
1960:
1930:
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1622:
1611:
natural language processing library which includes implementations of popular string metrics
1562:
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1446:
1405:
1357:
1308:
1228:
889:
865:
39:
504:
1813:
1754:
1666:
1515:"A fast bit-vector algorithm for approximate string matching based on dynamic programming"
1022:
881:
864:
Traditionally, approximate string matching algorithms are classified into two categories:
1591:
with recent advances in approximate string matching based on an edit distance threshold.
34:
A fuzzy
Mediawiki search for "angry emoticon" has as a suggested result "andré emotions"
1866:
1759:
1272:
Algorithms on strings, trees, and sequences: computer science and computational biology
966:
939:
935:
927:
835:
818:
817:) time with the dynamic programming algorithm, while the backwards-working phase takes
808:
641:, we can easily find a solution to the original problem: it is the substring for which
461:
1567:
1550:
1204:
17:
1980:
1676:
1653:
1427:
Zobel, Justin; Dart, Philip (1995). "Finding approximate matches in large lexicons".
1361:
1320:
1248:
1017:
71:
1419:
1240:
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sequences has become an important application. Approximate matching is also used in
848:
pairs of strings. Widely used algorithms are based on filter-verification, hashing,
1879:
1696:
1541:
1458:
1329:
1889:
942:
is a common application where records from two disparate databases are matched.
907:
903:
1608:
1328:
Navarro, Gonzalo; Baeza-Yates, Ricardo; Sutinen, Erkki; Tarhio, Jorma (2001).
931:
1132:
1130:
1232:
986:
59:
1450:
1533:
1410:
1393:
1312:
1604:
1289:
Navarro, Gonzalo (2001). "A guided tour to approximate string matching".
74:
between the string and the pattern. The usual primitive operations are:
1925:
1594:
1012:
601:, and determine which one of them has the minimal edit distance to the
481:. It uses an alternative formulation of the problem: for each position
55:
751:) values, we then choose the minimal value in the last row, let it be
911:
895:. A review of on-line searching algorithms was done by G. Navarro.
930:. With the availability of large amounts of DNA data, matching of
892:
788:
is a substring of T with the minimal edit distance to the pattern
1909:
885:
853:
1618:
1136:
1583:
1049:
1047:
1045:
477:
A better solution, which was proposed by
Sellers, relies on
1614:
1105:
1103:
1101:
877:, being appropriate for dictionary fuzzy search only.
1174:"Fzf - A Quick Fuzzy File Search from Linux Terminal"
1064:
1062:
534:
507:
382:
326:
264:
926:
Common applications of approximate matching include
1918:
1865:
1832:
1799:
1778:
1720:
1652:
1477:Combinatorial Pattern Matching (CPM'96), LNCS 1075
1330:"Indexing Methods for Approximate String Matching"
1205:"Fast Approximate String Matching in a Dictionary"
1121:
558:
520:
437:
368:
312:
27:Finding strings that approximately match a pattern
1601:library of string metrics and phonetic algorithms
497:, compute the minimum edit distance between the
453:, has the smallest edit distance to the pattern
1053:
1630:
1589:Efficient Similarity Query Processing Project
1274:. Cambridge, UK: Cambridge University Press.
1080:
8:
1551:"Algorithms for approximate string matching"
1255:(2nd ed.). MIT Press. pp. 364–7.
1637:
1623:
1615:
438:{\displaystyle T_{j',j}=t_{j'}\dots t_{j}}
1566:
1484:
1440:
1409:
1394:"The string-to-string correction problem"
1302:
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506:
429:
411:
387:
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347:
337:
325:
304:
285:
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263:
1809:Comparison of regular-expression engines
1494:Galil, Zvi; Apostolico, Alberto (1997).
1109:
678:Levenshtein distance computing algorithm
29:
1160:
1092:
1068:
1041:
369:{\displaystyle T=t_{1}t_{2}\dots t_{n}}
1770:Zhu–Takaoka string matching algorithm
1203:Baeza-Yates, R.; Navarro, G. (1998).
184:Some approximate matchers also treat
7:
1498:. Oxford : Oxford University Press.
1221:Journal of Experimental Algorithmics
313:{\displaystyle P=p_{1}p_{2}...p_{m}}
1735:Boyer–Moore string-search algorithm
724: − 1) in computing
46:(often colloquially referred to as
254:Problem formulation and algorithms
25:
1824:Nondeterministic finite automaton
1765:Two-way string-matching algorithm
1429:Software: Practice and Experience
609:. Write this minimal distance as
501:first characters of the pattern,
1392:Wagner, R.; Fischer, M. (1974).
1214:. IEEE CS Press. pp. 14–22.
1004:for fuzzy and non-fuzzy matching
657:being the length of the pattern
605:first characters of the pattern
593:, go through all substrings of
50:) is the technique of finding
1740:Boyer–Moore–Horspool algorithm
1730:Apostolico–Giancarlo algorithm
1337:IEEE Data Engineering Bulletin
1122:Baeza-Yates & Navarro 1998
1025:for Semantic Similarity Search
449:, which, of all substrings of
1:
1568:10.1016/S0019-9958(85)80046-2
1479:. Irvine, CA. pp. 1–23.
218:differs by one substitution,
1745:Knuth–Morris–Pratt algorithm
1672:Damerau–Levenshtein distance
1362:10.1016/0196-6774(80)90016-4
1251:; Leiserson, Rivest (2001).
739:In the array containing the
242:will count as matches while
1936:Compressed pattern matching
1662:Approximate string matching
1496:Pattern matching algorithms
1054:Cormen & Leiserson 2001
952:A common command-line tool
44:approximate string matching
2013:
1987:String matching algorithms
1941:Longest common subsequence
1852:Needleman–Wunsch algorithm
1722:String-searching algorithm
1377:(1st ed.). Springer.
1253:Introduction to Algorithms
992:Needleman–Wunsch algorithm
982:Locality-sensitive hashing
850:Locality-sensitive hashing
1951:Sequential pattern mining
1791:Commentz-Walter algorithm
1779:Multiple string searching
1712:Wagner–Fischer algorithm
1081:Wagner & Fischer 1974
712: − 1) or
1961:String rewriting systems
1946:Longest common substring
1857:Smith–Waterman algorithm
1682:Gestalt pattern matching
1008:Smith–Waterman algorithm
559:{\displaystyle T_{j',j}}
1895:Generalized suffix tree
1819:Thompson's construction
1555:Information and Control
1375:Algorithm Design Manual
1233:10.1145/1963190.1963191
947:acoustic fingerprinting
860:On-line versus off-line
1847:Hirschberg's algorithm
1513:Myers, G. (May 1999).
1451:10.1002/spe.4380250307
1373:Skiena, Steve (1998).
1270:Gusfield, Dan (1997).
570:that ends at position
560:
522:
439:
370:
314:
48:fuzzy string searching
35:
18:Fuzzy string searching
1702:Levenshtein automaton
1692:Jaro–Winkler distance
1534:10.1145/316542.316550
1411:10.1145/321796.321811
1350:Journal of Algorithms
1313:10.1145/375360.375365
1291:ACM Computing Surveys
1149:Zobel & Dart 1995
972:Jaro–Winkler distance
720: − 1,
700: − 1,
561:
523:
521:{\displaystyle P_{i}}
440:
371:
315:
226:by one deletion, and
33:
1750:Rabin–Karp algorithm
1707:Levenshtein distance
1595:StringMetric project
1549:Ukkonen, E. (1985).
997:Plagiarism detection
977:Levenshtein distance
875:Levenshtein distance
585:, and each position
532:
528:, and any substring
505:
380:
324:
262:
1997:Dynamic programming
1905:Ternary search tree
1137:Navarro et al. 2001
1002:Regular expressions
871:dynamic programming
621:). After computing
597:ending at position
479:dynamic programming
376:, find a substring
1834:Sequence alignment
1801:Regular expression
1522:Journal of the ACM
1398:Journal of the ACM
577:For each position
556:
518:
489:and each position
435:
366:
320:and a text string
310:
222:by one insertion,
36:
1974:
1973:
1966:String operations
1505:978-0-19-511367-9
1384:978-0-387-94860-7
1281:978-0-521-58519-4
1262:978-0-262-03293-3
16:(Redirected from
2004:
1992:Pattern matching
1931:Pattern matching
1885:Suffix automaton
1687:Hamming distance
1639:
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1616:
1584:Flamingo Project
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1814:Regular grammar
1795:
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1755:Raita algorithm
1716:
1667:Bitap algorithm
1648:
1643:
1605:Natural project
1580:
1575:
1561:(1–3): 100–18.
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1468:Further reading
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1023:Vector database
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589:in the pattern
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1578:External links
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1486:10.1.1.42.1593
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795:Computing the
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1110:Gusfield 1997
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