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Consensus Patterns (Probably) Has no EPTAS

  • Christina Boucher
  • Christine Lo
  • Daniel Lokshantov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)

Abstract

Given n length-L strings S = {s1, …, s n } over a constant size alphabet Σ together with an integer ℓ, where ℓ ≤ L, the objective of Consensus Patterns is to find a length-ℓ string s, a substring t i of each s i in S such that ∑  ∀ id(t i , s) is minimized. Here d(x, y) denotes the Hamming distance between the two strings x and y. Consensus Patterns admits a PTAS  [Li et al., JCSS 2002] is fixed parameter tractable when parameterized by the objective function value [Marx, SICOMP 2008], and although it is a well-studied problem, improvement of the PTAS to an EPTAS seemed elusive. We prove that Consensus Patterns does not admit an EPTAS unless FPT=W[1], answering an open problem from [Fellows et al., STACS 2002, Combinatorica 2006]. To the best of our knowledge, Consensus Patterns is the first problem that admits a PTAS, and is fixed parameter tractable when parameterized by the value of the objective function but does not admit an EPTAS under plausible complexity assumptions. The proof of our hardness of approximation result combines parameterized reductions and gap preserving reductions in a novel manner.

Keywords

Parameterized Complexity Binary String Parameterized Problem Polynomial Time Approximation Scheme Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Christina Boucher
    • 1
  • Christine Lo
    • 2
  • Daniel Lokshantov
    • 3
  1. 1.Department of Computer ScienceColorado State University in Fort CollinsFort CollinsUSA
  2. 2.Department of Computer Science and EngineeringUniversity of California at San DiegoSan DiegoUSA
  3. 3.Department of InformaticsUniversity of BergenBergenNorway

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