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181
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 418 (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
Learning String Edit Distance
, 1997
"... In many applications, it is necessary to determine the similarity of two strings. A widelyused notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one string into the other. In this report, we provide a stochastic mo ..."
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Cited by 198 (2 self)
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In many applications, it is necessary to determine the similarity of two strings. A widelyused notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one string into the other. In this report, we provide a stochastic model for string edit distance. Our stochastic model allows us to learn a string edit distance function from a corpus of examples. We illustrate the utility of our approach by applying it to the difficult problem of learning the pronunciation of words in conversational speech. In this application, we learn a string edit distance with nearly one fifth the error rate of the untrained Levenshtein distance. Our approach is applicable to any string classification problem that may be solved using a similarity function against a database of labeled prototypes.
Optimal alignments in linear space
 CABIOS
, 1988
"... Space, not time, is often the limiting factor when computing optimal sequence alignments, and a number of recent papers in the biology literature have proposed spacesaving strategies. However, a 1975 computer science paper by Hirschberg presented a method that is superior to the newer proposals, bo ..."
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Cited by 183 (3 self)
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Space, not time, is often the limiting factor when computing optimal sequence alignments, and a number of recent papers in the biology literature have proposed spacesaving strategies. However, a 1975 computer science paper by Hirschberg presented a method that is superior to the newer proposals, both in theory and in practice. The goal of this note is to give Hirschberg’s idea the visibility it deserves by developing a linearspace version of Gotoh’s algorithm, which accommodates affine gap penalties. A portable Csoftware package implementing this algorithm is available on the BIONET free of charge.
An O(ND) Difference Algorithm and Its Variations
 Algorithmica
, 1986
"... The problems of finding a longest common subsequence of two sequences A and B and a shortest edit script for transforming A into B have long been known to be dual problems. In this paper, they are shown to be equivalent to finding a shortest/longest path in an edit graph. Using this perspective, a s ..."
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Cited by 159 (4 self)
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The problems of finding a longest common subsequence of two sequences A and B and a shortest edit script for transforming A into B have long been known to be dual problems. In this paper, they are shown to be equivalent to finding a shortest/longest path in an edit graph. Using this perspective, a simple O(ND) time and space algorithm is developed where N is the sum of the lengths of A and B and D is the size of the minimum edit script for A and B. The algorithm performs well when differences are small (sequences are similar) and is consequently fast in typical applications. The algorithm is shown to have O(N +D expectedtime performance under a basic stochastic model. A refinement of the algorithm requires only O(N) space, and the use of suffix trees leads to an O(NlgN +D ) time variation.
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 141 (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 77 (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.
The String Edit Distance Matching Problems with Moves
, 2006
"... The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smalles ..."
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Cited by 60 (3 self)
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The edit distance between two strings S and R is defined to be the minimum number of character inserts, deletes and changes needed to convert R to S. Given a text string t of length n, and a pattern string p of length m, informally, the string edit distance matching problem is to compute the smallest edit distance between p and substrings of t. We relax the problem so that (a) we allow an additional operation, namely, substring moves, and (b) we allow approximation of this string edit distance. Our result is a near linear time deterministic algorithm to produce a factor of O(log n log ∗ n) approximation to the string edit distance with moves. This is the first known significantly subquadratic algorithm for a string edit distance problem in which the distance involves nontrivial alignments. Our results are obtained by embedding strings into L1 vector space using a simplified parsing technique we call Edit
A Subquadratic Sequence Alignment Algorithm for Unrestricted Cost Matrices
, 2002
"... The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n 2 ) time. We address the challenge of computing the similarity of two strings in subquadratic time, for metrics which use a scoring ..."
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Cited by 56 (4 self)
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The classical algorithm for computing the similarity between two sequences [36, 39] uses a dynamic programming matrix, and compares two strings of size n in O(n 2 ) time. We address the challenge of computing the similarity of two strings in subquadratic time, for metrics which use a scoring matrix of unrestricted weights. Our algorithm applies to both local and global alignment computations. The speedup is achieved by dividing the dynamic programming matrix into variable sized blocks, as induced by LempelZiv parsing of both strings, and utilizing the inherent periodic nature of both strings. This leads to an O(n 2 = log n) algorithm for an input of constant alphabet size. For most texts, the time complexity is actually O(hn 2 = log n) where h 1 is the entropy of the text. Institut GaspardMonge, Universite de MarnelaVallee, Cite Descartes, ChampssurMarne, 77454 MarnelaVallee Cedex 2, France, email: mac@univmlv.fr. y Department of Computer Science, Haifa University, Haifa 31905, Israel, phone: (9724) 8240103, FAX: (9724) 8249331; Department of Computer and Information Science, Polytechnic University, Six MetroTech Center, Brooklyn, NY 112013840; email: landau@poly.edu; partially supported by NSF grant CCR0104307, by NATO Science Programme grant PST.CLG.977017, by the Israel Science Foundation (grants 173/98 and 282/01), by the FIRST Foundation of the Israel Academy of Science and Humanities, and by IBM Faculty Partnership Award. z Department of Computer Science, Haifa University, Haifa 31905, Israel; On Education Leave from the IBM T.J.W. Research Center; email: michal@cs.haifa.il; partially supported by by the Israel Science Foundation (grants 173/98 and 282/01), and by the FIRST Foundation of the Israel Academy of Science ...
Comparing hierarchical data in external memory
 In 25th Very Large Data Base Conference (VLDB
, 1999
"... We present an externalmemory algorithm for computing a minimumcost edit script between two rooted, ordered, labeled trees. The I/O, RAM, and CPU costs of our algorithm are, respectively, 4mn+7m+5n, 6S, andO(MN+(M+N)S1:5), whereMandNare the input tree sizes,Sis the block size,m=M=S, andn=N=S. This ..."
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Cited by 53 (2 self)
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We present an externalmemory algorithm for computing a minimumcost edit script between two rooted, ordered, labeled trees. The I/O, RAM, and CPU costs of our algorithm are, respectively, 4mn+7m+5n, 6S, andO(MN+(M+N)S1:5), whereMandNare the input tree sizes,Sis the block size,m=M=S, andn=N=S. This algorithm can make effective use of surplus RAM capacity to quadratically reduce I/O cost. We extend to trees the commonly used mapping from sequence comparison problems to shortestpath problems in edit graphs. 1
Algorithms and Complexity for Annotated Sequence Analysis
, 1999
"... Molecular biologists use algorithms that compare and otherwise analyze sequences that represent genetic and protein molecules. Most of these algorithms, however, operate on the basic sequence and do not incorporate the additional information that is often known about the molecule and its pieces. Thi ..."
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Cited by 41 (1 self)
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Molecular biologists use algorithms that compare and otherwise analyze sequences that represent genetic and protein molecules. Most of these algorithms, however, operate on the basic sequence and do not incorporate the additional information that is often known about the molecule and its pieces. This research describes schemes to combinatorially annotate this information onto sequences so that it can be analyzed in tandem with the sequence; the overall result would thus reflect both types of information about the sequence. These annotation schemes include adding colours and arcs to the sequence. Colouring a sequence would produce a samelength sequence of colours or other symbols that highlight or label parts of the sequence. Arcs can be used to link sequence symbols (or coloured substrings) to indicate molecular bonds or other relationships. Adding these annotations to sequence analysis problems such as sequence alignment or finding the longest common subsequence can make the problem more complex, often depending on the complexity of the annotation scheme. This research examines the different annotation schemes and the corresponding problems of verifying annotations, creating annotations, and finding the longest common subsequence of pairs of sequences with annotations. This work involves both the conventional complexity framework and parameterized complexity, and includes algorithms and hardness results for both frameworks. Automata and transducers are created for some annotation verification and creation problems. Different restrictions on layered substring and arc annotation are considered to de iii termine what properties an annotation scheme must have to make its incorporation feasible. Extensions to the algorithms that use weighting schemes are explored. Examin...