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35
Algorithms for the longest common subsequence problem
 J. ACM
, 1977
"... AaS~ACT Two algorithms are presented that solve the longest common subsequence problem The first algorithm is applicable in the general case and requires O(pn + n log n) time where p is the length of the longest common subsequence The second algorithm requires time bounded by O(p(m + 1 p)log n) In ..."
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Cited by 179 (2 self)
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AaS~ACT Two algorithms are presented that solve the longest common subsequence problem The first algorithm is applicable in the general case and requires O(pn + n log n) time where p is the length of the longest common subsequence The second algorithm requires time bounded by O(p(m + 1 p)log n) In the common speoal case where p is close to m, this algorithm takes much less time than n ~ KEY WORDS AND PHRASES ' subsequence, common subsequence, algorithm CR CATEOORIES 3 73, 3 79, 5 25, 5 39
Meaningful Change Detection in Structured Data
 IN PROCEEDINGS OF THE ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 1997
"... Detecting changes by comparing data snapshots is an important requirement for difference queries, active databases, and version and configuration management. In this paper we focus on detecting meaningful changes in hierarchically structured data, such as nestedobject data. This problem is much mor ..."
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Cited by 118 (8 self)
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Detecting changes by comparing data snapshots is an important requirement for difference queries, active databases, and version and configuration management. In this paper we focus on detecting meaningful changes in hierarchically structured data, such as nestedobject data. This problem is much more challenging than the corresponding one for relational or flatfile data. In order to describe changes better, we base our work not just on the traditional "atomic" insert, delete, update operations, but also on operations that move an entire subtree of nodes, and that copy an entire subtree. These operations allows us to describe changes in a semantically more meaningful way. Since this change detection problem is NPhard, in this paper we present a heuristic change detection algorithm that yields close to "minimal" descriptions of the changes, and that has fewer restrictions than previous algorithms. Our algorithm is based on transforming the change detection problem to a problem of com...
Exact and Approximation Algorithms for Sorting By Reversals, With Application to Genome Rearrangement
, 1995
"... Motivated by the problem in computational biology of reconstructing the series of chromosome inversions by which one organism evolved from another, we consider the problem of computing the shortest series of reversals that transform one permutation to another. The permutations describe the order of ..."
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Cited by 78 (4 self)
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Motivated by the problem in computational biology of reconstructing the series of chromosome inversions by which one organism evolved from another, we consider the problem of computing the shortest series of reversals that transform one permutation to another. The permutations describe the order of genes on corresponding chromosomes, and a reversal takes an arbitrary substring of elements and reverses their order. For this problem we develop two algorithms: a greedy approximation algorithm that finds a solution provably close to optimal in O(n 2 ) time and O(n) space for an n element permutation, and a branch and bound exact algorithm that finds an optimal solution in O(mL(n;n)) time and O(n 2 ) space, where m is the size of the branch and bound search tree and L(n; n) is the time to solve a linear program of n variables and n constraints. The greedy algorithm is the first to come within a constant factor of the optimum; it guarantees a solution that uses no more than twice the min...
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 51 (11 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
Block Edit Models for Approximate String Matching
 Theoretical Computer Science
, 1997
"... In this paper we examine string block edit distance, in which two strings A and B are compared by extracting collections of substrings and placing them into correspondence. This model accounts for certain phenomena encountered in important realworld applications, including pen computing and molecu ..."
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Cited by 49 (4 self)
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In this paper we examine string block edit distance, in which two strings A and B are compared by extracting collections of substrings and placing them into correspondence. This model accounts for certain phenomena encountered in important realworld applications, including pen computing and molecular biology. The basic problem admits a family of variations depending on whether the strings must be matched in their entireties, and whether overlap is permitted. We show that several variants are NPcomplete, and give polynomialtime algorithms for solving the remainder. Keywords: block edit distance, approximate string matching, sequence comparison, approximate ink matching, dynamic programming. 1 Introduction The edit distance model for string comparison [Lev66, NW70, WF74] has found widespread application in fields ranging from molecular biology to bird song classification [SK83]. A great deal of research has been devoted to this area, and numerous algorithms have been proposed for com...
Treetotree Correction for Document Trees
, 1995
"... Documents can be represented as ordered labelled trees. Finding the editing distance between documents is a particular case of the general problem for trees. We give a detailed survey of previous results, presenting them in a single notation to elucidate their commonalities. We then discuss two ways ..."
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Cited by 22 (0 self)
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Documents can be represented as ordered labelled trees. Finding the editing distance between documents is a particular case of the general problem for trees. We give a detailed survey of previous results, presenting them in a single notation to elucidate their commonalities. We then discuss two ways of extending these resultsfirst, by changing the set of primitive editing operations used by existing algorithms and, second, by postprocessing the output of the algorithms to recognize patterns of change significant to documents. Finally, we provide extensions of the first type. Our algorithm allows subtree operations but is otherwise similar to that of Zhang and Shasha. This is a corrected and expanded version of Technical Report 91315. y This report was completed during a sabbatical at INRIA (Institute National de Recherche en Informatique et en Automatique) in Rocquencourt, France. Contents 1 Introduction 3 2 Background 5 2.1 StringtoString Correction: Wagner and Fischer ...
Pattern Matching with Swaps
, 1997
"... Let a text string T of n symbols and a pattern string P of m symbols from alphabet \Sigma be given. A swapped version T 0 of T is a length n string derived from T by a series of local swaps, (i.e. t 0 ` / t `+1 and t 0 `+1 / t ` ) where each element can participate in no more than one swap. ..."
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Cited by 19 (8 self)
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Let a text string T of n symbols and a pattern string P of m symbols from alphabet \Sigma be given. A swapped version T 0 of T is a length n string derived from T by a series of local swaps, (i.e. t 0 ` / t `+1 and t 0 `+1 / t ` ) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all locations i for which there exists a swapped version T 0 of T where there is an exact matching of P in location i of T 0 . It has been an open problem whether swapped matching can be done in less than O(mn) time. In this paper we show the first algorithm that solves the pattern matching with swaps problem in time o(mn). We present an algorithm whose time complexity is O(nm 1=3 log m log 2 min(m; j\Sigmaj)) for a general alphabet \Sigma. Key Words: Design and analysis of algorithms, combinatorial algorithms on words, pattern matching, pattern matching with swaps, nonstandard pattern matching. Department of Mathematics...
Overlap Matching
 Information and Computation
, 2001
"... We propose a new paradigm for string matching, namely structural matching. In structural matching, the text and pattern contents are not important. Rather, some areas in the text and patterns are singled out, say intervals. A "match" is a text location where a specified relation between ..."
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Cited by 19 (5 self)
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We propose a new paradigm for string matching, namely structural matching. In structural matching, the text and pattern contents are not important. Rather, some areas in the text and patterns are singled out, say intervals. A "match" is a text location where a specified relation between the text and pattern areas is satisfied. In particular we define the structural matching problem of Overlap (Parity) Matching. We seek the text locations where all overlaps of the given pattern and text intervals have even length. We show that this problem can be solved in time O(n log m), where the text length is n and the pattern length is m. As an application of overlap matching, we show how to reduce the String Matching with Swaps problem to the overlap matching problem. The String Matching with Swaps problem is the problem of string matching in the presence of local swaps. The best known deterministic upper bound for this problem was O(nm 1/3 log m log #) for a general alphabet #, wher...
Sequence similarity: a nonaligning technique
 Sociological Methods and Research
, 2003
"... This article reviews objections to optimalmatching (OM) algorithms in sequence analysis and reformulates the concept ofsequence similarity in terms ofa binary precedence relation. This precedence relation is then used to develop a new quantification of sequence similarity. The new measure is used t ..."
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Cited by 13 (0 self)
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This article reviews objections to optimalmatching (OM) algorithms in sequence analysis and reformulates the concept ofsequence similarity in terms ofa binary precedence relation. This precedence relation is then used to develop a new quantification of sequence similarity. The new measure is used to reanalyze the life history data that were previously discussed by Dijkstra and Taris (1995). The reanalysis demonstrates the new measure to be superior to the OM algorithm and the alternatives proposed by Dijkstra and Taris. A new algorithm is presented to enumerate matching ktuples from pairs of sequences in polynomial time.
Crossing number of graphs with rotation systems
, 2005
"... We show that computing the crossing number of a graph with a given rotation system is NPcomplete. This result leads to a new and much simpler proof of Hliněn´y’s result, that computing the crossing number of a cubic graph (without rotation system) is NPcomplete. We also investigate the special ca ..."
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Cited by 6 (3 self)
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We show that computing the crossing number of a graph with a given rotation system is NPcomplete. This result leads to a new and much simpler proof of Hliněn´y’s result, that computing the crossing number of a cubic graph (without rotation system) is NPcomplete. We also investigate the special case of multigraphs with rotation systems on a fixed number k of vertices. For k =1andk = 2 the crossing number can be computed in polynomial time and approximated to within a factor of 2 in linear time. For larger k we show how to approximate the crossing number to within a factor of ( k+4 4 m edges. /5intimeO(m k+2) on a graph with