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83
A Guided Tour to Approximate String Matching
 ACM Computing Surveys
, 1999
"... We survey the current techniques to cope with the problem of string matching allowing 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 t ..."
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Cited by 404 (38 self)
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We survey the current techniques to cope with the problem of string matching allowing 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 according to each case. We conclude with some future work directions and open problems. 1
OnLine Construction of Suffix Trees
, 1995
"... An online algorithm is presented for constructing the suffix tree for a given string in time linear in the length of the string. The new algorithm has the desirable property of processing the string symbol by symbol from left to right. It has always the suffix tree for the scanned part of the strin ..."
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Cited by 327 (2 self)
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An online algorithm is presented for constructing the suffix tree for a given string in time linear in the length of the string. The new algorithm has the desirable property of processing the string symbol by symbol from left to right. It has always the suffix tree for the scanned part of the string ready. The method is developed as a lineartime version of a very simple algorithm for (quadratic size) suffix tries. Regardless of its quadratic worstcase this latter algorithm can be a good practical method when the string is not too long. Another variation of this method is shown to give in a natural way the wellknown algorithms for constructing suffix automata (DAWGs).
Compressed suffix arrays and suffix trees with applications to text indexing and string matching (extended abstract
 in Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing
, 2000
"... Abstract. The proliferation of online text, such as found on the World Wide Web and in online databases, motivates the need for spaceefficient text indexing methods that support fast string searching. We model this scenario as follows: Consider a text T consisting of n symbols drawn from a fixed al ..."
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Cited by 189 (17 self)
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Abstract. The proliferation of online text, such as found on the World Wide Web and in online databases, motivates the need for spaceefficient text indexing methods that support fast string searching. We model this scenario as follows: Consider a text T consisting of n symbols drawn from a fixed alphabet Σ. The text T can be represented in n lg Σ  bits by encoding each symbol with lg Σ  bits. The goal is to support fast online queries for searching any string pattern P of m symbols, with T being fully scanned only once, namely, when the index is created at preprocessing time. The text indexing schemes published in the literature are greedy in terms of space usage: they require Ω(n lg n) additional bits of space in the worst case. For example, in the standard unit cost RAM, suffix trees and suffix arrays need Ω(n) memory words, each of Ω(lg n) bits. These indexes are larger than the text itself by a multiplicative factor of Ω(lg Σ  n), which is significant when Σ is of constant size, such as in ascii or unicode. On the other hand, these indexes support fast searching, either in O(m lg Σ) timeorinO(m +lgn) time, plus an outputsensitive cost O(occ) for listing the occ pattern occurrences. We present a new text index that is based upon compressed representations of suffix arrays and suffix trees. It achieves a fast O(m / lg Σ  n +lgɛ Σ  n) search time in the worst case, for any constant
Reducing the Space Requirement of Suffix Trees
 Software – Practice and Experience
, 1999
"... We show that suffix trees store various kinds of redundant information. We exploit these redundancies to obtain more space efficient representations. The most space efficient of our representations requires 20 bytes per input character in the worst case, and 10.1 bytes per input character on average ..."
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Cited by 118 (10 self)
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We show that suffix trees store various kinds of redundant information. We exploit these redundancies to obtain more space efficient representations. The most space efficient of our representations requires 20 bytes per input character in the worst case, and 10.1 bytes per input character on average for a collection of 42 files of different type. This is an advantage of more than 8 bytes per input character over previous work. Our representations can be constructed without extra space, and as fast as previous representations. The asymptotic running times of suffix tree applications are retained. Copyright © 1999 John Wiley & Sons, Ltd. KEY WORDS: data structures; suffix trees; implementation techniques; space reduction
Speeding Up Two StringMatching Algorithms
 ALGORITHMICA
, 1994
"... We show how to speed up two stringmatching algorithms: the BoyerMoore algorithm (BM algorithm), and its version called here the reverse factor algorithm (RF algorithm). The RF algorithm is based on factor graphs for the reverse of the pattern.The main feature of both algorithms is that they scan ..."
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Cited by 96 (18 self)
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We show how to speed up two stringmatching algorithms: the BoyerMoore algorithm (BM algorithm), and its version called here the reverse factor algorithm (RF algorithm). The RF algorithm is based on factor graphs for the reverse of the pattern.The main feature of both algorithms is that they scan the text righttoleft from the supposed right position of the pattern. The BM algorithm goes as far as the scanned segment (factor) is a suffix of the pattern. The RF algorithm scans while the segment is a factor of the pattern. Both algorithms make a shift of the pattern, forget the history, and start again. The RF algorithm usually makes bigger shifts than BM, but is quadratic in the worst case. We show that it is enough to remember the last matched segment (represented by two pointers to the text) to speed up the RF algorithm considerably (to make a linear number of inspections of text symbols, with small coefficient), and to speed up the BM algorithm (to make at most 2.n comparisons). Only a constant additional memory is needed for the search phase. We give alternative versions of an accelerated RF algorithm: the first one is based on combinatorial properties of primitive words, and the other two use the power of suffix trees extensively. The paper demonstrates the techniques to transform algorithms, and also shows interesting new applications of data structures representing all subwords of the pattern in compact form.
Transducers and repetitions
 Theoretical Computer Science
, 1986
"... Abstract. The factor transducer of a word associates to each of its factors (or subwc~rds) their first occurrence. Optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given. Analogue results and a simple algorithm are given for the case of subseq ..."
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Cited by 94 (19 self)
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Abstract. The factor transducer of a word associates to each of its factors (or subwc~rds) their first occurrence. Optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given. Analogue results and a simple algorithm are given for the case of subsequential suffix transducers. Algorithms are applied to repetition searching in words. Rl~sum~. Le transducteur des facteurs d'un mot associe a chacun de ses facteurs leur premiere occurrence. On donne des bornes optimales sur la taille du transducteur minimal d'un mot ainsi qu'un algorithme pour sa construction. On donne des r6sultats analogues et un algorithme simple dans le cas du transducteur souss~luentiel des suffixes d'un mot. On donne une application la d6tection de r6p6titions dans les mots. Contents
Finite automata
 Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter 1
, 1990
"... ..."
From Ukkonen to McCreight and Weiner: A Unifying View of LinearTime Suffix Tree Construction
 Algorithmica
, 1997
"... We review the linear time suffix tree constructions by Weiner, McCreight, and Ukkonen. We use the terminology of the most recent algorithm, Ukkonen's online construction, to explain its historic predecessors. This reveals relationships much closer than one would expect, since the three algorithms ar ..."
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Cited by 66 (6 self)
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We review the linear time suffix tree constructions by Weiner, McCreight, and Ukkonen. We use the terminology of the most recent algorithm, Ukkonen's online construction, to explain its historic predecessors. This reveals relationships much closer than one would expect, since the three algorithms are based on rather different intuitive ideas. Moreover, it completely explains the differences between these algorithms in terms of simplicity, efficiency, and implementation complexity.
Complete inverted files for efficient text retrieval and analysis
 Journal of the ACM
, 1987
"... Abstract. Given a finite set of texts S = (wi, *.., wk) over some fixed finite alphabet 2, a complete inverted tile for S is an abstract data type that provides the functionsfind ( which returns the longest prefix of w that occurs (as a subword of a word) in S, freq(w), which returns the number of t ..."
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Cited by 59 (1 self)
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Abstract. Given a finite set of texts S = (wi, *.., wk) over some fixed finite alphabet 2, a complete inverted tile for S is an abstract data type that provides the functionsfind ( which returns the longest prefix of w that occurs (as a subword of a word) in S, freq(w), which returns the number of times w occurs in S, and locations(w), which returns the set of positions where w occurs in S. A data structure. that implements a complete inverted file for S that occupies linear space and can be built in linear time, using the uniformcost RAM model, is given. Using this data structure, the time for each of the above query functions is optimal. To accomplish this, techniques from the theory of finite automata and the work on suffix trees are used to build a deterministic finite automaton that recognizes the set of all subwords of the set S. This automaton is then annotated with additional information and compacted to facilitate the desired query functions. The result is a data structure that is smaller and more flexible than the s&ix tree.