The problem of finding a constrained longest common subsequence (CLCS) for the sequences A and B with respect to the sequence P was introduced recently. Its goal is to find a longestsubsequence C of A and B such that...
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The problem of finding a constrained longest common subsequence (CLCS) for the sequences A and B with respect to the sequence P was introduced recently. Its goal is to find a longestsubsequence C of A and B such that P is a subsequence of C. Most of the algorithms solving the CLCS problem are based on dynamic programming. Bit-parallelism is a technique of using single bits in a machine word for concurrent computation. We propose the first bit-parallel algorithm computing a CLCS and/or its length which outperforms the other known algorithms in terms of speed.
We consider a variant of the classical longestcommonsubsequence problem called Doubly-constrained longest common subsequence (DC-LCS). Given two strings s(1) and s(2) over an alphabet Sigma, a set C-s of strings, an...
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We consider a variant of the classical longestcommonsubsequence problem called Doubly-constrained longest common subsequence (DC-LCS). Given two strings s(1) and s(2) over an alphabet Sigma, a set C-s of strings, and a function C-0 : Sigma -> N, the DC-LCS problem consists of finding the longestsubsequence s of s(1) and s(2) such that s is a supersequence of all the strings in C-s and such that the number of occurrences in s of each symbol sigma is an element of Sigma is upper bounded by C-0(sigma). The DC-LCS problem provides a clear mathematical formulation of a sequence comparison problem in Computational Biology and generalizes two other constrained variants of the LCS problem that have been introduced previously in the literature: the constrained LCS and the Repetition-Free LCS. We present two results for the DC-LCS problem. First, we illustrate a fixed-parameter algorithm where the parameter is the length of the solution which is also applicable to the more specialized problems. Second, we prove a parameterized hardness result for the constrained LCS problem when the parameter is the number of the constraint strings (vertical bar C-s vertical bar) and the size of the alphabet Sigma E. This hardness result also implies the parameterized hardness of the DC-LCS problem (with the same parameters) and its NP-hardness when the size of the alphabet is constant. 2010 Elsevier B.V. All rights reserved.
A common operation on strings is to calculate a value of similarity. The longestcommonsubsequence (LCS) is a measure of similarity between two sequences. An extension of LCS measure is the constrainedlongestcommon...
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ISBN:
(纸本)9781728108834
A common operation on strings is to calculate a value of similarity. The longestcommonsubsequence (LCS) is a measure of similarity between two sequences. An extension of LCS measure is the constrained longest common subsequence (CLCS). The CLCS consists of calculating the LCS of two sequences, and it is a supersequence of a constrained sequence. This paper is an experimental evaluation of the most important CLCS algorithms. The implemented algorithms have a similar performance and were tested with different kinds of random strings belonging to the alphabets: generated uniformly at random (4, 10, 20, 32, 48 and 64 characters) and English text (239 characters). This study could help in selecting optimal algorithms for a given problem.
Given two strings X and Y and a constraining string P, a string Z is called a constrained longest common subsequence of X and Y with respect to P if Z is the longestcommonsubsequence of X and Y such that P is a subs...
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Given two strings X and Y and a constraining string P, a string Z is called a constrained longest common subsequence of X and Y with respect to P if Z is the longestcommonsubsequence of X and Y such that P is a subsequence of Z. In this paper, we propose an O(r x min{mN, nM})-time algorithm for solving this problem, where m, n and r are the lengths of X, Y and P, respectively, and M and N are the number of runs of the run-length-encoded strings of X and Y, respectively.
The problem of finding a longestcommonsubsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrainedlongest co...
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The problem of finding a longestcommonsubsequence of two main sequences with some constraint that must be a substring of the result (STR-IC-LCS) was formulated recently. It is a variant of the constrained longest common subsequence problem. As the known algorithms for the STR-IC-LCS problem are cubic-time, the presented quadratic-time algorithm is significantly faster. (C) 2012 Elsevier B.V. All rights reserved.
In this paper we address the constrained longest common subsequence problem. Given two sequences X, Y and a constrained sequence P, a sequence Z is a constrained longest common subsequence for X and Y with respect to ...
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In this paper we address the constrained longest common subsequence problem. Given two sequences X, Y and a constrained sequence P, a sequence Z is a constrained longest common subsequence for X and Y with respect to P if Z is the longestsubsequence of X and Y such that P is a subsequence of Z. Recently, Tsai [Inform. Process. Lett. 88 (2003) 173-176] proposed an O(n(2 .) m(2 .) r) time algorithm to solve this problem using dynamic programming technique, where n, m and r are the lengths of X, Y and P, respectively. In this paper, we present a simple algorithm to solve the constrained longest common subsequence problem in O(n (.) m (.) r) time and show that the constrained longest common subsequence problem is equivalent to a special case of the constrained multiple sequence alignment problem which can also be solved with the same time complexity. (C) 2004 Published by Elsevier B.V.
The longestcommonsubsequence (LCS) problem is a well-known and studied problem in computer science and bioinformatics. It consists in finding the longestsubsequence that is common to two or more given sequences. In...
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The longestcommonsubsequence (LCS) problem is a well-known and studied problem in computer science and bioinformatics. It consists in finding the longestsubsequence that is common to two or more given sequences. In this article, we address the problem of finding all LCS for the Sequential Substring constrainedLCS (SSCLCS) problem, called the Multiple SSCLCS problem. To solve this problem, we first propose a dominant point-based sequential algorithm, designed on a new Leveled Direct Acyclic Graph (DAG) that gives the correct evaluation order of subproblems to avoid redundancy due to overlap. Depending on whether the constraints may overlap or not, it requires O ( S |Sigma| K + 1 + r + n |Sigma|) and O ( S |Sigma| K + 1 + n |Sigma|) time with O(Max_level+n|Sigma|) space. S is the number of partial SSCLCS in a node, K is the number of DAG levels, n is the length of sequences, r is the total length of constraints, Max_level is the number of nodes in the largest level of the DAG, and |Sigma| is the length of the alphabet. Then, we derive a coarse-grained multicomputer parallel solution requiring O ( S | Sigma| K +1 + r + n |Sigma | ) and O ( S | Sigma|K+1+n |Sigma | pp ) execution time, O(Max_level + n |Sigma |) memory space and O ( K ) communication rounds. p is the number of processors. Experimental results showed that the parallel algorithm is, respectively, 14.43x and 19.19x faster than the sequential algorithm on 32 and 64 processors.
In this paper, we present linear-time algorithms for the construction two novel types of finite automata and show how they can be used to efficiently solve the longestcommonsubsequence (LCS), Shortest common Superse...
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In this paper, we present linear-time algorithms for the construction two novel types of finite automata and show how they can be used to efficiently solve the longestcommonsubsequence (LCS), Shortest common Supersequence (SCS) and constrained longest common subsequence (CLCS) problems for degenerate strings. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, new parallel algorithms based on the Coarse-Grained Multicomputer (CGM) model for solving the longestcommonsubsequence (LCS) problem with a string exclusion constraint (STR-EC-LCS) is presented. Based...
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ISBN:
(纸本)9781538678794
In this paper, new parallel algorithms based on the Coarse-Grained Multicomputer (CGM) model for solving the longestcommonsubsequence (LCS) problem with a string exclusion constraint (STR-EC-LCS) is presented. Based on a previous sequential algorithm, we propose two CGM parallel algorithms for STR-EC-LCS problem. We perform an experimental study of our two solutions to validate our theoretical predictions, and conclude that our first algorithm that minimizes idleness of the processors is better than the second. To the best of our knowledge, these algorithms are the first CGMbased parallel algorithms for the generalized-constrained-LCS problem.
One of the most fundamental methods for comparing two given strings A and B is the longestcommonsubsequence (LCS), where the task is to find (the length) of the longestcommonsubsequence. In this paper, we address ...
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ISBN:
(纸本)9783031231001;9783031231018
One of the most fundamental methods for comparing two given strings A and B is the longestcommonsubsequence (LCS), where the task is to find (the length) of the longestcommonsubsequence. In this paper, we address the STR-IC-LCS problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A, B, and P, if Z is one of the longestcommonsubsequences of A and B that contains P as a substring. We present a space efficient solution for the STR-IC-LCS problem. Our algorithm computes the length of an STR-IC-LCS in O(n(2)) time and O((l + 1)(n - l + 1)) space where l is the length of a longestcommonsubsequence of A and B of length n. When l = O(1) or n - l = O(1), then our algorithm uses only linear O(n) space.
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