An all-substrings common subsequence algorithm

Alves, Carlos Eduardo Rodrigues; Cáceres, Edson Norberto; Song, Siang Wun

doi:10.1016/j.endm.2005.05.019

Cited by 16 publications

(26 citation statements)

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“…In this paper, we propose the first all semi-local LCS algorithm, which runs in subquadratic time O ( mn log 0.5 (m+n) ) when m and n are reasonably close. This improves on [2] simultaneously in algorithm functionality, output representation efficiency, and running time.…”

Section: Introductionmentioning

confidence: 90%

“…The standard dynamic programming approach can be regarded as comparing all prefixes of each string against all prefixes of the other string. Papers [2,7,[13][14][15][16]20] present several variations on the theme of comparing substrings (prefixes, suffixes) of two strings. In [13,15], the two input strings are revealed character by character.…”

Section: Previous Workmentioning

confidence: 99%

“…It is well known (see e.g. [2,16] and references therein) that all essential information in the alignment 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 linearsize representation of the string comparison dag, and a standard computational geometry problem known as dominance counting.…”

Section: Introductionmentioning

confidence: 99%

“…If the output lengths of the all semi-local LCS problem are represented explicitly, the total size of the output is ((m + n) 2 ), corresponding to m 2 + n 2 possible substrings and 2mn possible prefix-suffix pairs. To reduce the storage requirements, we allow the output lengths to be represented implicitly by a smaller data structure that allows efficient retrieval of individual output values.…”

Section: Introductionmentioning

confidence: 99%

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Semi-local longest common subsequences in subquadratic time

Tiskin

2008

Journal of Discrete Algorithms

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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 ((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., based on previous work by Schmidt, 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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Section: Introductionmentioning

confidence: 90%

Section: Previous Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semi-local longest common subsequences in subquadratic time

Tiskin

2008

Journal of Discrete Algorithms

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“…Based on [15], we present an algorithm to solve the ALCS problem that takes O(n a n b ) time and O(n b ) space. A short version of this paper appeared in [5].…”

Section: Introductionmentioning

confidence: 97%

An all-substrings common subsequence algorithm

Alves

Cáceres

Song

2008

Discrete Applied Mathematics

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Given two strings A and B of lengths n a and n b , n a n b , respectively, the all-substrings longest common subsequence (ALCS) problem obtains, for every substring B of B, the length of the longest string that is a subsequence of both A and B . The ALCS problem has many applications, such as finding approximate tandem repeats in strings, solving the circular alignment of two strings and finding the alignment of one string with several others that have a common substring. We present an algorithm to prepare the basic data structure for ALCS queries that takes O(n a n b ) time and O(n a + n b ) space. After this preparation, it is possible to build a matrix of size O(n 2 b ) that allows any LCS length to be retrieved in constant time. Some trade-offs between the space required and the querying time are discussed. To our knowledge, this is the first algorithm in the literature for the ALCS problem.

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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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An all-substrings common subsequence algorithm

Cited by 16 publications

References 0 publications

Semi-local longest common subsequences in subquadratic time

Semi-local longest common subsequences in subquadratic time

An all-substrings common subsequence algorithm

All Semi-local Longest Common Subsequences in Subquadratic Time

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