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

  • Authors:

  • Jianxin Wang;Jianer Chen;Min Huang

  • Affiliations:

  • School of Information Science and Engineering, Central South University, Changsha 410083, The People's Republic of China;School of Information Science and Engineering, Central South University, Changsha 410083, The People's Republic of China and Department of Computer Science, Texas A&M University, College Station, ...;School of Information Science and Engineering, Central South University, Changsha 410083, The People's Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2008

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Abstract

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/@e)n^o^(^1^/^@e^) 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 @e. 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 @e.