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A Fast and Practical BitVector Algorithm for the Longest Common Subsequence Problem
 Information Processing Letters
, 2000
"... This paper presents a new practical bitvector algorithm for solving the well known Longest Common Subsequence (LCS) problem. Given two strings of length m and n, n m, we present an algorithm which determines the length p of an LCS in O(nm=w) time and O(m=w) space, where w is the number of bits in a ..."
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Cited by 25 (2 self)
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This paper presents a new practical bitvector algorithm for solving the well known Longest Common Subsequence (LCS) problem. Given two strings of length m and n, n m, we present an algorithm which determines the length p of an LCS in O(nm=w) time and O(m=w) space, where w is the number of bits in a machine word. This algorithm can be thought of as columnwise "parallelization" of the classical dynamic programming approach. Our algorithm is very efficiently in practice, where computing the length of an LCS of two strings can be done in linear time and constant (additional/working) space by assuming that m w.
Matching for RunLength Encoded Strings
, 1999
"... this paper, we develop significantly faster algorithms for a special class of strings which emerge frequently in pattern matching problems. A string S is runlength encoded if it is described as an ordered sequence of pairs (oe; i), each consisting of an alphabet symbol oe and an integer i. Each pai ..."
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Cited by 22 (2 self)
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this paper, we develop significantly faster algorithms for a special class of strings which emerge frequently in pattern matching problems. A string S is runlength encoded if it is described as an ordered sequence of pairs (oe; i), each consisting of an alphabet symbol oe and an integer i. Each pair corresponds to a run in S consisting of i consecutive occurrences of oe. For example, the string
String Editing and Longest Common Subsequences
 In Handbook of Formal Languages
, 1996
"... this paper, in view of the particularly rich variety of algorithmic solutions that have been devised for this problem over the past two decades or so, which made it susceptible to some degrees of unification and systematization of independent and general interest. Our discussion starts with the expo ..."
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Cited by 15 (2 self)
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this paper, in view of the particularly rich variety of algorithmic solutions that have been devised for this problem over the past two decades or so, which made it susceptible to some degrees of unification and systematization of independent and general interest. Our discussion starts with the exposition of two basic approaches to LCS computation, due respectively to Hirschberg [1978] and Hunt and Szymanski [1977]. We then discuss faster implementations of this second paradigm, and the data strucures that support them. In Section 5. we discuss algorithms that use only linear space to compute an LCS and yet do not necessarily take \Theta(nm) time. One, final, such algorithm is presented in section 6. where many of the ideas and tools accumulated in the course of our discussion find employment together. In Section 7. we make return to string editing in its general formulation and discuss some of its efficient solutions within a parallel model of computation.
Serial Computations of Levenshtein Distances
, 1997
"... sequence (LCS) of those strings. If D is the simple Levenshtein distance between two strings having lengths m and n, SES is the length of the shortest edit sequence between the strings, and L is the length of an LCS of the strings, then SES = D and L = (m + n 0D)=2. We will focus on the problem of ..."
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Cited by 14 (0 self)
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sequence (LCS) of those strings. If D is the simple Levenshtein distance between two strings having lengths m and n, SES is the length of the shortest edit sequence between the strings, and L is the length of an LCS of the strings, then SES = D and L = (m + n 0D)=2. We will focus on the problem of determining the length of an LCS and also on the related problem of recovering an LCS. Another related problem, which will be discussed in Chapter 7, is that of approximate string matching, in which it is desired to locate all positions within string y which begin an approximation to string x containing at most D errors (insertions or deletions). 124 SERIAL COMPUTATIONS OF LEVENSHTEIN DISTANCES procedure CLASSIC( x,<
BitParallel LCSlength Computation Revisited
 In Proc. 15th Australasian Workshop on Combinatorial Algorithms (AWOCA
, 2004
"... The longest common subsequence (LCS) is a classic and wellstudied measure of similarity between two strings A and B. This problem has two variants: determining the length of the LCS (LLCS), and recovering an LCS itself. In this paper we address the first of these two. Let m and n denote the leng ..."
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Cited by 7 (4 self)
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The longest common subsequence (LCS) is a classic and wellstudied measure of similarity between two strings A and B. This problem has two variants: determining the length of the LCS (LLCS), and recovering an LCS itself. In this paper we address the first of these two. Let m and n denote the lengths of the strings A and B, respectively, and w denote the computer word size. First we give a slightly improved formula for the bitparallel O(#m/w#n) LLCS algorithm of Crochemore et al. [4]. Then we discuss the relative performance of the bitparallel algorithms and compare our variant against one of the best conventional LLCS algorithms. Finally we propose and evaluate an O(#d/w#n) version of the algorithm, where d is the simple (indel) edit distance between A and B.
Sequence Comparison: Some Theory and Some Practice
, 1988
"... A brief survey of the theory and practice of sequence comparison is made focusing on diff, the UNIX 1 file difference utility. 1 Sequence comparison Sequence comparison is a deep and fascinating subject in Computer Science, both theoretical and practical. However, in our opinion, neither the theo ..."
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Cited by 7 (0 self)
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A brief survey of the theory and practice of sequence comparison is made focusing on diff, the UNIX 1 file difference utility. 1 Sequence comparison Sequence comparison is a deep and fascinating subject in Computer Science, both theoretical and practical. However, in our opinion, neither the theoretical nor the practical aspects of the problem are well understood and we feel that their mastery is a true challenge for Computer Science. The central problem can be stated very easily: find an algorithm, as efficient and practical as possible, to compute a longest common subsequence (lcs for short) of two given sequences 2 . As usual, a subsequence of a sequence is another sequence obtained from it by deleting some (not necessarily contiguous) terms. Thus, both en/pri and en/pai are longest common subsequences of sequence/comparison and theory/and/practice. Part of this work was done while the author was visiting the Universit'e de Rouen, in 1987. That visit was partially supported...