On the Common Substring Alignment Problem

Landau, Gad M.; Ziv-Ukelson, Michal

doi:10.1006/jagm.2001.1191

Cited by 38 publications

(50 citation statements)

References 25 publications

(30 reference statements)

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“…Each incremental update takes time O(n log l) per occurrence of the common substring c in the pattern a, and O(n) per character of a outside any occurrence of c. Overall, the algorithm takes time O(n) for the first occurrence of the common substring c in a pattern, and time O(n log l) for each subsequent occurrence of c in the same pattern. In particular, if the common substring occurs only once in every pattern string, our algorithm improves on the algorithm of [77,33] in functionality, without any increase in the asymptotic running time.…”

Section: Common-substring Lcs and Semi-local Lcsmentioning

confidence: 97%

“…The common-substring LCS problem was introduced by Landau et al [77,33]. Given a text string b of length n and an unspecified number of pattern strings, the problem asks for the LCS score of the text against each of the patterns.…”

Section: Common-substring Lcs and Semi-local Lcsmentioning

confidence: 99%

“…An improved algorithm is given in [77,33]. This algorithm, following some preprocessing in time O(nl), runs in time O(n) for each occurrence of the common substring.…”

Section: Common-substring Lcs and Semi-local Lcsmentioning

confidence: 99%

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Semi-local String Comparison: Algorithmic Techniques and Applications

Tiskin

2008

Math.comput.sci.

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The longest common subsequence (LCS) problem is a classical problem in computer science. The semi-local LCS problem is a generalisation of the LCS problem, arising naturally in the context of string comparison. In this work, we present a number of algorithmic techniques related to the semi-local LCS problem, and give a number of algorithmic applications of these techniques. Summarising the presented results, we conclude that semilocal string comparison turns out to be a useful algorithmic plug-in, which unifies, and often improves on, a number of previous approaches to various substring-and subsequence-related problems.

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Section: Common-substring Lcs and Semi-local Lcsmentioning

confidence: 97%

Section: Common-substring Lcs and Semi-local Lcsmentioning

confidence: 99%

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Semi-local String Comparison: Algorithmic Techniques and Applications

Tiskin

2008

Math.comput.sci.

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“…Therefore, the computation is performed essentially on substrings of subsequent inputs. In [13], multiple strings sharing a common substring are compared against a common target string. A common feature in many of these algorithms is the use of linear-sized string comparison dag representation, and a suitable merging procedure that "stitches together" the representations of neighbouring dag blocks to obtain a representation for the blocks' union.…”

Section: Previous Workmentioning

confidence: 99%

“…It is well-known (see e.g. [13,1] and references therein) that all essential information in the grid dag can in fact be represented by a data structure of size O(m + n). In this paper, we expose a rather surprising (and to the best of our knowledge, previously unnoticed) connection between this linear-size representation of the string comparison dag, and a standard computational geometry problem known as dominance counting.…”

Section: Introductionmentioning

confidence: 99%

All Semi-local Longest Common Subsequences in Subquadratic Time

Tiskin

2006

Computer Science – Theory and Applications

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Abstract. For two strings a, b of lengths m, n respectively, the longest common subsequence (LCS) problem consists in comparing a and b by computing the length of their LCS. In this paper, we define a generalisation, called "the all semi-local LCS problem", where each string is compared against all substrings of the other string, and all prefixes of each string are compared against all suffixes of the other string. An explicit representation of the output lengths is of size Θ (m+n) 2 . We show that the output can be represented implicitly by a geometric data structure of size O(m + n), allowing efficient queries of the individual output lengths. The currently best all string-substring LCS algorithm by Alves et al. can be adapted to produce the output in this form. We also develop the first all semi-local LCS algorithm, running in time o(mn) when m and n are reasonably close. Compared to a number of previous results, our approach presents an improvement in algorithm functionality, output representation efficiency, and/or running time.

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On the Complexity of Sparse Exon Assembly

Kent

Landau

Ziv-Ukelson

2005

Combinatorial Pattern Matching

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Abstract. Gene structure prediction is one of the most important problems in computational molecular biology. A combinatorial approach to the problem, denoted Gene Prediction via Spliced Alignment, was introduced by Gelfand, Mironov and Pevzner [5]. The method works by finding a set of blocks in a source genomic sequence S whose concatenation (splicing) fits a target gene T belonging to a homologous species. Let S,T and the candidate exons be sequences of size O(n). The innovative algorithm described in [5] yields an O(n 3 ) result for spliced alignment, regardless of filtration mode. In this paper we suggest a new algorithm which targets the case where filtering has been applied to the data, resulting in a set of O(n) candidate exon blocks. Our algorithm yields an O(n 2 √ n) solution for this case.

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On the Common Substring Alignment Problem

Cited by 38 publications

References 25 publications

Semi-local String Comparison: Algorithmic Techniques and Applications

Semi-local String Comparison: Algorithmic Techniques and Applications

All Semi-local Longest Common Subsequences in Subquadratic Time

On the Complexity of Sparse Exon Assembly

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