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88
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 585 (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.
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 190 (2 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 90 (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 D&sup2;) for general weighting edit operations and in time O(N_1 N_2 D &radic;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 84 (25 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...
Faster Algorithms for String Matching with k Mismatches
 J. OF ALGORITHMS
, 2000
"... The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T . Currently, the fastest algorithms for this problem are the following. The LandauVishkin algorithm finds all locations where the pat ..."
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Cited by 70 (15 self)
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The string matching with mismatches problem is that of finding the number of mismatches between a pattern P of length m and every length m substring of the text T . Currently, the fastest algorithms for this problem are the following. The LandauVishkin algorithm finds all locations where the pattern has at most k errors (where k is part of the input) in time O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time O(n p m log m). We present
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 67 (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
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 66 (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...
A Faster Algorithm for Approximate String Matching
 Algorithmica
, 1996
"... . 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 O(log n), being n the maxi ..."
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Cited by 64 (28 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 O(log n), being n the maximum size of the text. The running time achieved is O(n) for small patterns (i.e. of length m = O( p log n)), independently of the maximum number of errors allowed, k. This algorithm is then used to design two general algorithms. One of them partitions the problem into subproblems, while the other partitions the automaton into subautomata. These algorithms are combined to obtain a hybrid algorithm which on average is O(n) for moderate k=m ratios, O( p mk= log n n) for medium ratios, and O((m \Gamma k)kn= log n) for large ratios. We show experimentally that this hybrid algorithm is faster than previous ones for moderate size of patterns and error ratios, which is the case in text search...
Algorithms for Computing Approximate Repetitions in Musical Sequences
 International Journal of Computer Mathematics
, 1999
"... Here we introduce two new notions of approximate matching with application in computer assisted music analysis. We present algorithms for each notion of approximation: for approximate string matching and for computing approximate squares. ..."
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Cited by 57 (16 self)
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Here we introduce two new notions of approximate matching with application in computer assisted music analysis. We present algorithms for each notion of approximation: for approximate string matching and for computing approximate squares.