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Information Processing Letters
Fixed-parameter tractability and completeness II: on completeness for W[1]
Theoretical Computer Science
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SIAM Journal on Computing
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STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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Journal of the ACM (JACM)
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Communications of the ACM
A linear space algorithm for computing maximal common subsequences
Communications of the ACM
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Communications of the ACM
How hard is computing the edit distance?
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ACM Computing Surveys (CSUR)
Introduction to Circuit Complexity: A Uniform Approach
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Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
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SIGAL '90 Proceedings of the International Symposium on Algorithms
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FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
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Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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ACM SIGACT News
Approximating Edit Distance Efficiently
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Parameterized Complexity
IEEE Transactions on Computers
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Given a string x and a language L, the Hamming distance of x to L is the minimum Hamming distance of x to any string in L. The edit distance of a string to a language is analogously defined.First, we prove that there is a language in AC0 such that both Hamming and edit distance to this language are hard to approximate; they cannot be approximated with factor O(n(1/3)-ε), for any ε 0, unless P = NP (n denotes the length of the input string).Second, we show the parameterized intractability of computing the Hamming distance. We prove that for every t ∈ N there exists a language in AC0 for which computing the Hamming distance is W[t]-hard. Moreover, there is a language in P for which computing the Hamming distance is WP-hard.Then we show that the problems of computing the Hamming distance and of computing the edit distance are in some sense equivalent by presenting approximation ratio preserving reductions from the former to the latter and vice versa.Finally, we define HamP to be the class of languages to which the Hamming distance can efficiently, i.e. in polynomial time, be computed. We show some properties of the class HamP. On the other hand, we give evidence that a characterization in terms of automata or formal languages might be difficult.