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Fixed-Parameter Approximability and Hardness

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 52 Accesses

Years and Authors of Summarized Original Work

Footnote 1

  • 1995; Alon, Yuster, Zwick

  • 2005; Marx

  • 2006; McCartin

  • 2013; Hajiaghayi, Kortsarz

Problem Definition

NP-hard problems are believed to be intractable. This is the widely believed assumption that P ≠ NP. For all our problems, the size of their input is denoted by n. In parameterized complexity, the input is refined to (I, k) with k a parameter related to the input, and the goal is to find an exact algorithm for the problem that runs in time \(f(k) \cdot n^{O(1)}\), for some function f. In this survey, we parameterize by the optimum value of the instance unless stated otherwise. In addition, the optimum is always integral. In approximation algorithms, a ρ approximation for a minimization (maximization) problem P is a polynomial time algorithm A, such that for any instance I, A returns a solution of value A(I) and A(I)∕opt(I) ≤ ρ (opt(I)∕A(I) ≤ ρ) with opt(I) the optimum value for the instance. In both subjects, there are...

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Notes

  1. 1.

    Supported in part by NSF grant number 1218620.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Rutgers University, Camden, NJ, USA

    Guy Kortsarz

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  1. Guy Kortsarz
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Correspondence to Guy Kortsarz .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Kortsarz, G. (2016). Fixed-Parameter Approximability and Hardness. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_763

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