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About 436 papers for “Longest common subsequence problem”

THE LONGEST COMMON SUBSEQUENCE PROBLEM REVISITED

Purdue E-pubs, A. Apostolico, C. Guerra et al. · 1985

This paper fe-examines. in a unified framework, me problem of finding a longest------commoIr"StIbsequence-CJ:;eS)-oftWo--strings;-anct-proposes--simple-and-generally------------faster implementations for most known approaches. Let l be the length of an LCS between two strings of length m and n~. respectively, and let s be lhe alphabet size. The first revised strategy follows the paradigm of a previous 0 (in) time algoritlun by Hirschberg. The new version can be implemented in time O(fm-min{logs,logmJog(2nlm)}), which is profitable when the inpm strings differ considerably in size (a looser bound for both versions is 0 (mn ». A natural offspring of this algorilhrn is also presented which uses only linear space and has the same time bound. except for an additive term O(mlogm). \\vl1ile most exist-ing algorithms use li.1J.ear space in order to compute only l, the only previously known algorimm computing an LCS in linear space required never less than time 8(nm). AnoIher algorirh.m. presemed here improves on the Hunt·Szymanski algoriu.'un. This latter takes time o«r+n) logn), where r$mn is the total number of marches berween the cwo input silings. Such a performance is quire

Cited by 0

The Longest Common Exemplar Subsequence Problem

Shutao Zhang, Ruizhi Wang, Daming Zhu et al. · 2018

In this paper, we propose to find order conserved subsequences of genomes by finding longest common exemplar subsequences of the genomes. The longest common exemplar subsequence problem is given by two genomes, asks to find a common exemplar subsequence of them, such that the exemplar subsequence length is maximized. We focus on genomes whose genes of the same gene family are in at most s spans. We propose a dynamic programming algorithm with time complexity O(s4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sup> mn) to find a longest common exemplar subsequence of two genomes with one genome admitting s span genes of the same gene family, where m, n stand for the gene numbers of those two given genomes. Our algorithm can be extended to find longest common exemplar subsequences of more than one genomes.

Cited by 2

A Generalized Constrained Longest Common Subsequence Problem

Berger, Christoph · reposiTUm (TU Wien) · 2020

Diese Arbeit beschäftigt sich mit dem Constrained Longest Common Subsequence (CLCS) Problem, welches eingeführt wurde, um die Ähnlichkeit verschiedener biologischer Sequenzen zu messen. Dabei wird für eine gegebene Menge von beliebigen Strings die längste gemeinsame Teilfolge an Zeichen gesucht, welche selbst wiederum einen bestimmten gegebenen String als Teilfolge enthält. Es handelt sich um eine Variante des gut untersuchten Longest Common Subsequence (LCS) Problems. Verschiedene Algorithmen sind bekannt um das CLCS Problem für genau zwei Strings (2CLCS) zu lösen, das allgemeine mCLCS Problem mit einer beliebigen Menge von Strings wurde bisher jedoch nur näherungsweise mit einem Approximationsverfahren gelöst. Das mCLCS Problem kann in der Biologie der Identifikation von Molekülgruppen dienen, deren Moleküle eine Gemeinsamkeit in Form einer bestimmten vorhandenen Teilstruktur aufweisen. In dieser Arbeit werden mehrere neue Methoden vorgestellt um das mCLCS Problem effektiv zu lösen. Wir präsentieren eine heuristische Beam Search in der Form eines generellen Suchframeworks sowie einen exakten A*-Algorithmus. Die Ergebnisse unserer Tests zeigen, dass unsere A*-Suche, geführt von bekannten Upper Bounds des LCS Problems, signifikant schneller im Lösen von 2CLCS Instanzen als bisherige Algorithmen ist. Beim mCLCS Problem mit mehreren Strings konnten von der A*-Suche kleine bis mittelgroße Instanzen gelöst werden. Für jene Instanzen, die von A* nicht gelöst werden können, schlagen wir den Einsatz von Beam Search vor. Zur Führung der Beam Search haben sich eine auf Wahrscheinlichkeitstheorie basierenden Heuristik, sowie eine Heuristik zur Berechnung der erwarteten Länge als besonders effektiv erwiesen. Diese Beam Search Konfigurationen konnten bei fast allen von der A*-Suche exakt gelösten Instanzen ebenfalls optimale Lösungen finden und waren dabei signifikant schneller als die A*-Suche.

Cited by 0Open access

The repetition-free longest common subsequence problem

Christian Tjandraatmadja · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2010

Exploramos o seguinte problema: dadas duas sequências X e Y sobre um alfabeto finito, encontre uma subsequência comum máxima de X e Y sem símbolos repetidos. Estudamos a estrutura deste problema, particularmente do ponto de vista de grafos e de combinatória poliédrica. Desenvolvemos algoritmos de aproximação e heurísticas para este problema. O enfoque deste trabalho está na construção de um algoritmo baseado na técnica branch-and-cut, aproveitando-nos de um algoritmo de separação eficiente e de heurísticas e técnicas para encontrarmos uma solução ótima mais cedo. Também estudamos um problema mais fácil no qual este problema é baseado: dadas duas sequências X e Y sobre um alfabeto finito, encontre uma subsequência comum máxima de X e Y. Exploramos este problema do ponto de vista de combinatória poliédrica e descrevemos vários algoritmos conhecidos para resolvê-lo.

Cited by 0

The merged longest common increasing subsequence problem

C. A. Lee, Chang‐Biau Yang, Kuo-Si Huang · Theoretical Computer Science · 2025

The merged longest common increasing subsequence (MLCIS) problem represents a generalized variant by combining the merged longest common subsequence (merged LCS, MLCS) problem and the longest increasing subsequence (LIS) problem. Given a pair of numeric sequences A and B along with a target numeric sequence T , the MLCIS problem aims to identify the longest common subsequence that is increasing in both the merged sequence E ( A , B ) and the target sequence T . Here, E ( A , B ) represents a new sequence constructed from arbitrarily merging A and B while maintaining their original orders. In this paper, we propose two algorithms for solving the MLCIS problem: dynamic programming and diagonal. The dynamic programming algorithm has a time complexity of O( mnr ), where m , n and r denote the lengths of sequences A , B and T , respectively. The time complexity of the diagonal algorithm is O( ( L + 1 ) ( r − L + 1 ) ( m + n ) ), where L denotes the length of the MLCIS answer. In general, as the experimental results show, the diagonal algorithm is more efficient than the dynamic programming algorithm in practice. Furthermore, the diagonal algorithm is very efficient when L is either very small or L is close to r , which coincides with the theoretical time complexity. • This paper defines the merged longest common increasing subsequence (MLCIS) problem. • The MLCIS problem is a combined generalization of the merged LCS and the longest increasing subsequence (LIS) problems. • We solve the problem with two approaches: dynamic programming and diagonal methods. • In the diagonal method, the number of elements in a cell is bounded by the maximal cardinality in the upper-left triangle. • The diagonal method is very efficient when the answer length is either very small or close to the target sequence length.

Cited by 0Open access

Approximating the longest approximate common subsequence problem

Wen‐Chen Hu, Gerhard X. Ritter, Mark S. Schmalz · 1998

Ah&act -Finding a kmgest common subsequence of two strings is a well4nown pmbktu We genemlize this ptvbkm to a longest approximate common subse!+wnceprobkm that produces a nuuhum-gain appnximate common subsequence of two strings. An apptvximate subsequence of a string X is a string edited from a subsequence of X String Z is an appnximate common subsequence of two strings X and Y if Z is an apptvximate subsequence of both X and Y. The gain jibnc* g assigns a nonnegatkve real number to each subsequence. The ptvbkm is divided into smaller segments in on&r to kssen its compkxity with some of these segments having been ptvven to be NP-hatd A heuristic apptvximation algorithm and an optimization neural network are constructed to jind a near-optimal solution for the ptobkm, where a ratio bound of the apptvximation algorithm is given, and a technique of interception is used to determke the values of the network weights. Some experimental msults and the comparative performance of the two methods also are discussed

Cited by 6Open access

Parallel Algorithms for the Longest Common Subsequence Problem

Lu, Mi · Figshare · 2021

A subsequence of a given string is any string obtained by deleting none or some symbols from the given string. A longest common subsequence of two strings is a common subsequence of both that is as long as any other common subsequences. The longest common subsequence problem is to find the longest common subsequence of two given strings. The bound on the complexity of this problem under the decision tree model is known as mn if the number of distinct symbols that can appear in strings is infinite, where m and n are the lengths of the two strings, respectively, and m ≤ n. In this paper, we propose two parallel algorithms for this problem on the CREWPRAM model. One takes O(log<sup>2</sup> m + log n) time with mn/ log m processors, which is faster than all the existing algorithms on the same model. The other takes O(log<sup>2</sup> m log log m) time with mn/ log<sup>2</sup> m log log m processors when log<sup>2</sup> m log log m &gt; log n, or otherwise O(log n) time with mn/ log n processors, which is optimal in the sense that the time x processors bound matches the complexity bound of the problem. Both algorithms exploit nice properties of the LCS problem that are discovered in this paper.

Cited by 0Open access

Parallel Algorithms for the Longest Common Subsequence Problem

Lu, Mi · Figshare · 2021

subsequence of a given string is any string obtainedby deleting none or some symbols from the given string.A longest common subsequence of two strings is a commonsubsequence of both that is as long as any other common subsequences. The longest common subsequence problem is to find the longest common subsequence of two given strings. The bound on the complexity of this problem under the decision tree model is known as mn if the number of distinct symbols that can appear in strings is infinite, where m and n are the lengths of the two strings, respectively, and m ≤ n. In this paper, we propose two parallel algorithms for this problem on the CREW-PRAM model. One takes O(log<sup>2</sup> m + log n) time with mn/ log m processors, which is faster than all the existing algorithms on the same model. The other takes O(log<sup>2</sup> m log log m) time with mn/ log<sup>2</sup> m log log m processors when log<sup>2</sup> m log log m &gt; log n, or otherwise O(log n) time with mn/ log n processors, which isoptimal in the sense that the time x processors bound matches the complexity bound of the problem. Both algorithms exploit nice properties of the LCS problem that are discovered in this paper.

Cited by 0Open access

Beam-ACO for the longest common subsequence problem

Christian Blum · QRU Quaderns de Recerca en Urbanisme · 2010

The longest common subsequence problem is classical string problem. It has applications, for example, in pattern recognition and bioinformatics. In this work we present a so-called Beam-ACO approach for solving this problem. Beam-ACO algorithms are hybrid techniques that results from a combination of ant colony optimization and beam search, which is an incomplete branch and bound derivative. Our results show that Beam-ACO is able to find new best solutions for 31 out of 60 benchmark instances that we chose for the experimental evaluation of the algorithm.

Cited by 13Open access

Systolic algorithms for the longest common subsequence problem

Chang‐Biau Yang, R. C. T. Lee · Journal of the Chinese Institute of Engineers · 1987

Abstract The concept of systolic array processors is very suitable for VLSI implementation. In this paper, we propose two systolic algorithms to solve the longest common subsequence problem by dynamic programming approach and also prove that these two algorithms are correct. The order of the time‐processor‐product of our algorithms is equal to that of the corresponding sequential method.

Cited by 26

An Optimal Algorithm for the Longest Common Subsequence Problem

Lu, Mi · Figshare · 2021

The longest common subsequence problem is to find a longest common subsequence of two given strings. The complexity of this problem on the decision tree model is known as mn, where m and n are the lengths of these two strings, respectively, and m ≤ n. We present a parallel algorithm for this problem on the CREW PRAM model, which takes O(log<sup>2</sup>m log log m) time with mn / log<sup>2</sup>m log log m processors when log<sup>2</sup> m log log m &gt; log n, or otherwise O(log n) time with mn / log n processors.

Cited by 0Open access

Mean-Field Approximations to the Longest Common Subsequence Problem

de Monvel, J. Boutet · arXiv (Cornell University) · 1998

The Longest Common Subsequence (LCS) problem is a fundamental problem of sequence comparison. A natural approximation to this problem is a model in which every pairs of letters of two ``sequences'' are matched independently of the other pairs with probability 1/S, $S$ representing the size of the alphabet. This model is analogous to a mean field version of the LCS problem, which can be solved with a cavity approach (Eur. Phys. J. B 7-2(1999),pp. 293-308). We refine here this approximation by incorporating in a systematic way correlations among the matches in the cavity calculation. We obtain a series of closer and closer approximations to the LCS problem, which we quantify in the large $S$ limit, both with a perturbative approach and by Monte-Carlo simulations. We find that, as it happens in the expansion around mean-field for other disordered systems, the corrections to our approximations depend upon long-ranged correlation effects which render the large $S$ expansion non-perturbative.

Cited by 0Open access

Heuristic Algorithms for the Longest Filled Common Subsequence Problem

Radu Stefan Mincu, Alexandru Popa · arXiv (Cornell University) · 2018

At CPM 2017, Castelli et al. define and study a new variant of the Longest Common Subsequence Problem, termed the Longest Filled Common Subsequence Problem (LFCS). For the LFCS problem, the input consists of two strings A and B and a multiset of characters M. The goal is to insert the characters from M into the string B, thus obtaining a new string B*, such that the Longest Common Subsequence (LCS) between A and B* is maximized. Casteli et al. show that the problem is NP-hard and provide a 3/5-approximation algorithm for the problem. In this paper we study the problem from the experimental point of view. We introduce, implement and test new heuristic algorithms and compare them with the approximation algorithm of Casteli et al. Moreover, we introduce an Integer Linear Program (ILP) model for the problem and we use the state of the art ILP solver, Gurobi, to obtain exact solution for moderate sized instances.

Cited by 0Open access