The parameterized complexity of sequence alignment and consensus
Theoretical Computer Science
An integrated complexity analysis of problems from computational biology
An integrated complexity analysis of problems from computational biology
Bounds on the Complexity of the Longest Common Subsequence Problem
Journal of the ACM (JACM)
The Complexity of Some Problems on Subsequences and Supersequences
Journal of the ACM (JACM)
The Longest Common Subsequence Problem for Small Alphabet Size Between Many Strings
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Two Algorithms for the Longest Common Subsequence of Three (or More) Strings
CPM '92 Proceedings of the Third Annual Symposium on Combinatorial Pattern Matching
Computing the similarity of two sequences with nested arc annotations
Theoretical Computer Science
Longest common subsequence problem for unoriented and cyclic strings
Theoretical Computer Science
Some Approximations for Shortest Common Nonsubsequences and Supersequences
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
On parameterized complexity of the Multi-MCS problem
Theoretical Computer Science
The Parameterized Complexity of k-Flip Local Search for SAT and MAX SAT
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Improved Approximation Results on the Shortest Common Supersequence Problem
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Complexities of the centre and median string problems
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
A probabilistic beam search approach to the shortest common supersequence problem
EvoCOP'07 Proceedings of the 7th European conference on Evolutionary computation in combinatorial optimization
Parameterized complexity and approximability of the SLCS problem
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Efficient stochastic local search algorithm for solving the shortest common supersequence problem
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Variants of constrained longest common subsequence
Information Processing Letters
Evolutionary-based iterative local search algorithm for the shortest common supersequence problem
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Editing graphs to satisfy degree constraints: A parameterized approach
Journal of Computer and System Sciences
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
W-hardness under linear FPT-reductions: structural properties and further applications
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Lower bounds and parameterized approach for longest common subsequence
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Memetic algorithms with partial lamarckism for the shortest common supersequence problem
IWINAC'05 Proceedings of the First international work-conference on the Interplay Between Natural and Artificial Computation conference on Artificial Intelligence and Knowledge Engineering Applications: a bioinspired approach - Volume Part II
A comparison of evolutionary approaches to the shortest common supersequence problem
IWANN'05 Proceedings of the 8th international conference on Artificial Neural Networks: computational Intelligence and Bioinspired Systems
Parameterized problems on coincidence graphs
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
The parameterized complexity of k-flip local search for SAT and MAX SAT
Discrete Optimization
Parameterized complexity and approximability of the Longest Compatible Sequence problem
Discrete Optimization
The Multivariate Algorithmic Revolution and Beyond
FPT suspects and tough customers: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Hardness of longest common subsequence for sequences with bounded run-lengths
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
On the space complexity of parameterized problems
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Satisfiability of acyclic and almost acyclic CNF formulas
Theoretical Computer Science
Parameterized complexity results for exact bayesian network structure learning
Journal of Artificial Intelligence Research
Parameterized Domination in Circle Graphs
Theory of Computing Systems
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We show that the fixed alphabet shortest common supersequence (SCS) and the fixed alphabet longest common subsequence (LCS) problems parameterized in the number of strings are W[1]-hard. Unless W[1] = FPT, this rules out the existence of algorithms with time complexity of O(f(k)nα) for those problems. Here n is the size of the problem instance, α is constant, k is the number of strings and f is any function of k. The fixed alphabet version of the LCS problem is of particular interest considering the importance of sequence comparison (e.g. multiple sequence alignment) in the fixed length alphabet world of DNA and protein sequences.