New efficient algorithms for the LCS and constrained LCS problems

Authors:
Costas S. Iliopoulos;M. Sohel Rahman
Affiliations:
Algorithm Design Group, Department of Computer Science, King's College London, Strand, London WC2R 2LS, England, UK;Algorithm Design Group, Department of Computer Science, King's College London, Strand, London WC2R 2LS, England, UK
Venue:
Information Processing Letters
Year:
2008

Citing 11
Cited 12

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A fast algorithm for computing longest common subsequences

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A sub-quadratic sequence alignment algorithm for unrestricted cost matrices

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A simple algorithm for the constrained sequence problems

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A New Efficient Algorithm for Computing the Longest Common Subsequence

AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
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CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
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ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation

Finite automata based algorithms on subsequences and supersequences of degenerate strings

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Bit-Parallel Algorithm for the Constrained Longest Common Subsequence Problem

Fundamenta Informaticae
Finite automata based algorithms for the generalized constrained longest common subsequence problems

SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Restricted LCS

SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
On the generalized constrained longest common subsequence problems

Journal of Combinatorial Optimization
Regular language constrained sequence alignment revisited

IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Approximability of constrained LCS

Journal of Computer and System Sciences
Fast algorithms for computing the constrained LCS of run-length encoded strings

Theoretical Computer Science
Doubly-Constrained LCS and Hybrid-Constrained LCS problems revisited

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Efficient algorithms for the longest common subsequence problem with sequential substring constraints

Journal of Complexity
The substring inclusion constraint longest common subsequence problem can be solved in quadratic time

Journal of Discrete Algorithms
The constrained shortest common supersequence problem

Journal of Discrete Algorithms

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Abstract

In this paper, we study the classic and well-studied longest common subsequence (LCS) problem and a recent variant of it, namely the constrained LCS (CLCS) problem. In the CLCS problem, the computed LCS must also be a supersequence of a third given string. In this paper, we first present an efficient algorithm for the traditional LCS problem that runs in O(Rloglogn+n) time, where R is the total number of ordered pairs of positions at which the two strings match and n is the length of the two given strings. Then, using this algorithm, we devise an algorithm for the CLCS problem having time complexity O(pRloglogn+n) in the worst case, where p is the length of the third string.