An improved lower bound on approximation algorithms for the Closest Substring problem

The Closest Substring problem (the CSP problem) is a basic NP-hard problem in the study of computational biology. It is known that the problem has polynomial time approximation schemes. In this paper, we prove that unless the Exponential Time Hypothesis fails, the CSP problem has no polynomial time...

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Bibliographic Details
Published in:Information processing letters Vol. 107; no. 1; pp. 24 - 28
Main Authors: Wang, Jianxin, Chen, Jianer, Huang, Min
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 30.06.2008
Elsevier Science
Elsevier Sequoia S.A
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis of algorithms
Applied sciences
Approximation
Approximation algorithms
Approximations and expansions
Closest substring problem
Computational biology
Computer science; control theory; systems
Errors
Exact sciences and technology
Lower bound
Mathematical analysis
Mathematics
Miscellaneous
Sciences and techniques of general use
Studies
Theoretical computing
Closest substring problem
Lower bound
Approximation algorithms
Analysis of algorithms
Computational biology
Polynomial
Error estimation
Computer theory
Polynomial approximation
Biology
Approximation algorithm
Hypothesis
Polynomial time
NP hard problem
Information processing
Algorithm analysis
ISSN:0020-0190, 1872-6119
Online Access:Get full text
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Summary:The Closest Substring problem (the CSP problem) is a basic NP-hard problem in the study of computational biology. It is known that the problem has polynomial time approximation schemes. In this paper, we prove that unless the Exponential Time Hypothesis fails, the CSP problem has no polynomial time approximation schemes of running time f ( 1 / ε ) n o ( 1 / ε ) for any function f. This essentially excludes the possibility that the CSP problem has a practical polynomial time approximation scheme even for moderate values of the error bound ε. 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 problem for small error bound ε.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2007.12.005