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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 401 (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
A fast bitvector algorithm for approximate string matching based on dynamic programming
 J. ACM
, 1999
"... Abstract. The approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with korfewer differences. Simple and practical bitvector algorithms have been designed for this problem, most notably the one used in agrep. These alg ..."
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Cited by 137 (1 self)
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Abstract. The approximate string matching problem is to find all locations at which a query of length m matches a substring of a text of length n with korfewer differences. Simple and practical bitvector algorithms have been designed for this problem, most notably the one used in agrep. These algorithms compute a bit representation of the current stateset of the kdifference automaton for the query, and asymptotically run in either O(nmk/w) orO(nm log �/w) time where w is the word size of the machine (e.g., 32 or 64 in practice), and � is the size of the pattern alphabet. Here we present an algorithm of comparable simplicity that requires only O(nm/w) time by virtue of computing a bit representation of the relocatable dynamic programming matrix for the problem. Thus, the algorithm’s performance is independent of k, and it is found to be more efficient than the previous results for many choices of k and small m. Moreover, because the algorithm is not dependent on k, it can be used to rapidly compute blocks of the dynamic programming matrix as in the 4Russians algorithm of Wu et al. [1996]. This gives rise to an O(kn/w) expectedtime algorithm for the case where m may be arbitrarily large. In practice this new algorithm, that computes a region of the dynamic programming (d.p.) matrix w entries at a time using the basic algorithm as a subroutine, is significantly faster than our previous 4Russians algorithm, that computes the same region 4 or 5 entries at a time using table lookup. This performance improvement yields a code that is either superior or competitive with all existing algorithms except for some filtration algorithms that are superior when k/m is sufficiently small.
On the Editing Distance between Undirected Acyclic Graphs
, 1995
"... We consider the problem of comparing CUAL graphs (Connected, Undirected, Acyclic graphs with nodes being Labeled). This problem is motivated by the study of information retrieval for biochemical and molecular databases. Suppose we define the distance between two CUAL graphs G1 and G2 to be the weig ..."
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Cited by 75 (7 self)
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We consider the problem of comparing CUAL graphs (Connected, Undirected, Acyclic graphs with nodes being Labeled). This problem is motivated by the study of information retrieval for biochemical and molecular databases. Suppose we define the distance between two CUAL graphs G1 and G2 to be the weighted number of edit operations (insert node, delete node and relabel node) to transform G1 to G2. By reduction from exact cover by 3sets, one can show that finding the distance between two CUAL graphs is NPcomplete. In view of the hardness of the problem, we propose a constrained distance metric, called the degree2 distance, by requiring that any node to be inserted (deleted) have no more than 2 neighbors. With this metric, we present an efficient algorithm to solve the problem. The algorithm runs in time O(N_1 N_2 D²) for general weighting edit operations and in time O(N_1 N_2 D √D log D) for integral weighting edit operations, where N_i, i = 1, 2, is the number of nodes in G_i, D = min{d_1, d_2} and d_i is the maximum degree of G_i.
Faster Approximate String Matching
 Algorithmica
, 1999
"... We present a new algorithm for online approximate string matching. The algorithm is based on the simulation of a nondeterministic finite automaton built from the pattern and using the text as input. This simulation uses bit operations on a RAM machine with word length w = \Omega\Gamma137 n) bits, ..."
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Cited by 71 (24 self)
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We present a new algorithm for online approximate string matching. The algorithm is based on the simulation of a nondeterministic finite automaton built from the pattern and using the text as input. This simulation uses bit operations on a RAM machine with word length w = \Omega\Gamma137 n) bits, where n is the text size. This is essentially similar to the model used in Wu and Manber's work, although we improve the search time by packing the automaton states differently. The running time achieved is O(n) for small patterns (i.e. whenever mk = O(log n)), where m is the pattern length and k ! m the number of allowed errors. This is in contrast with the result of Wu and Manber, which is O(kn) for m = O(log n). Longer patterns can be processed by partitioning the automaton into many machine words, at O(mk=w n) search cost. We allow generalizations in the pattern, such as classes of characters, gaps and others, at essentially the same search cost. We then explore other novel techniques t...
An Extensible Framework for Data Cleaning
 In ICDE
, 2000
"... Data integration solutions dealing with large amounts of data have been strongly required in the last few years. Besides the traditional data integration problems (e.g. schema integration, local to global schema mappings), three additional data problems have to be dealt with: (1) the absence of un ..."
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Cited by 67 (0 self)
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Data integration solutions dealing with large amounts of data have been strongly required in the last few years. Besides the traditional data integration problems (e.g. schema integration, local to global schema mappings), three additional data problems have to be dealt with: (1) the absence of universal keys across dierent databases that is known as the object identity problem, (2) the existence of keyboard errors in the data, and (3) the presence of inconsistencies in data coming from multiple sources. Dealing with these problems is globally called the data cleaning process. In this work, we propose a framework which oers the fundamental services required by this process: data transformation, duplicate elimination and multitable matching. These services are implemented using a set of purposely designed macrooperators. Moreover, we propose an SQL extension for specifying each of the macrooperators. One important feature of the framework is the ability of explicitly includ...
A System for Approximate Tree Matching
, 1992
"... Ordered, labeled trees are trees in which each node has a label and the lefttoright order of its children (if it has any) is fixed. Such trees have many applications in vision, pattern recognition, molecular biology, programming compilation and natural language processing. Many of the applications ..."
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Cited by 61 (10 self)
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Ordered, labeled trees are trees in which each node has a label and the lefttoright order of its children (if it has any) is fixed. Such trees have many applications in vision, pattern recognition, molecular biology, programming compilation and natural language processing. Many of the applications involve comparing trees or retrieving/extracting information from a repository of trees. Examples include classification of unknown patterns, analysis of newly sequenced RNA structures, semantic taxonomy for dictionary definitions, generation of interpreters for nonprocedural programming languages, and automatic error recovery and correction for programming languages. Previous systems use exact matching (or generalized regular expression matching) for tree comparison. This paper presents a system, called ApproximateTreeByExample (ATBE), which allows inexact matching of trees. The ATBE system interacts with the user through a simple, but powerful query language; graphical devices a...
Approximate string matching over suffix trees
 PROCEEDINGS OF THE 4TH ANNUAL SYMPOSIUM ON COMBINATORIAL PATTERN MATCHING, NUMBER 684 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1993
"... The classical approximate stringmatching problem of finding the locations of approximate occurrences P 0 of pattern string P in text string T such that the edit distance between P and P 0 is k is considered. We concentrate on the special case in which T is available for preprocessing before the se ..."
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Cited by 55 (1 self)
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The classical approximate stringmatching problem of finding the locations of approximate occurrences P 0 of pattern string P in text string T such that the edit distance between P and P 0 is k is considered. We concentrate on the special case in which T is available for preprocessing before the searches with varying P and k. It is shown how the searches can be done fast using the suffix tree of T augmented with the suffix links as the preprocessed form of T and applying dynamic programming over the tree. Three variations of the search algorithm are developed with running times O(mq + n), O(mq log q + size of the output), and O(m
Indexing Methods for Approximate String Matching
 IEEE Data Engineering Bulletin
, 2000
"... Indexing for approximate text searching is a novel problem receiving much attention because of its applications in signal processing, computational biology and text retrieval, to name a few. We classify most indexing methods in a taxonomy that helps understand their essential features. We show that ..."
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Cited by 54 (10 self)
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Indexing for approximate text searching is a novel problem receiving much attention because of its applications in signal processing, computational biology and text retrieval, to name a few. We classify most indexing methods in a taxonomy that helps understand their essential features. We show that the existing methods, rather than completely different as they are regarded, form a range of solutions whose optimum is usually somewhere in between.
A Hybrid Indexing Method for Approximate String Matching
"... We present a new indexing method for the approximate string matching problem. The method is based on a suffix array combined with a partitioning of the pattern. We analyze the resulting algorithm and show that the average retrieval time is Ç Ò � ÐÓ � Ò,forsome�� that depends on the error fraction t ..."
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Cited by 54 (10 self)
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We present a new indexing method for the approximate string matching problem. The method is based on a suffix array combined with a partitioning of the pattern. We analyze the resulting algorithm and show that the average retrieval time is Ç Ò � ÐÓ � Ò,forsome�� that depends on the error fraction tolerated « and the alphabet size �. Itisshownthat �� for approximately « � � � Ô �,where � � � � ����. Thespace required is four times the text size, which is quite moderate for this problem. We experimentally show that this index can outperform by far all the existing alternatives for indexed approximate searching. These are also the first experiments that compare the different existing schemes.
Fast and Practical Approximate String Matching
 In Combinatorial Pattern Matching, Third Annual Symposium
, 1992
"... We present new algorithms for approximate string matching based in simple, but efficient, ideas. First, we present an algorithm for string matching with mismatches based in arithmetical operations that runs in linear worst case time for most practical cases. This is a new approach to string searchin ..."
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Cited by 53 (0 self)
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We present new algorithms for approximate string matching based in simple, but efficient, ideas. First, we present an algorithm for string matching with mismatches based in arithmetical operations that runs in linear worst case time for most practical cases. This is a new approach to string searching. Second, we present an algorithm for string matching with errors based on partitioning the pattern that requires linear expected time for typical inputs. 1 Introduction Approximate string matching is one of the main problems in combinatorial pattern matching. Recently, several new approaches emphasizing the expected search time and practicality have appeared [3, 4, 27, 32, 31, 17], in contrast to older results, most of them are only of theoretical interest. Here, we continue this trend, by presenting two new simple and efficient algorithms for approximate string matching. First, we present an algorithm for string matching with k mismatches. This problem consists of finding all instances o...