Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On the closest string and substring problems
Journal of the ACM (JACM)
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Parameterized Intractability of CLOSEST SUBSTRINGsize and Related Problems
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Distinguishing string selection problems
Information and Computation
Linear FPT reductions and computational lower bounds
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
W-hardness under linear FPT-reductions: structural properties and further applications
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Parameterized Complexity
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The Closest Substring problem (CSP), where a short string is sought that minimizes the number of mismatches between it and each of a given set of strings, is a minimization problem with polynomial time approximation schemes. In this paper, a lower bound on approximation algorithms for the CSP problem is developed. We prove that unless the Exponential Time Hypothesis (ETH Hypothesis, i.e., not all search problems in SNP are solvable in subexponential time) fails, the CSP problem has no polynomial time approximation schemes of running time f(1/Ɛ)|x|O(1/Ɛ) for any function f, where |x| is the size of input instance. This essentially excludes the possibility that the CSP problem has a practical polynomial time approximation scheme even for moderate values of the error bound Ɛ. As a consequence, it is unlikely that the study of approximation schemes for the CSP problem in the literature would lead to practical approximation algorithms for the CSP problem for small error bound Ɛ.