# Fixed-Parameter and Approximation Algorithms: A New Look

@article{Chitnis2013FixedParameterAA, title={Fixed-Parameter and Approximation Algorithms: A New Look}, author={Rajesh Hemant Chitnis and Mohammad Taghi Hajiaghayi and Guy Kortsarz}, journal={ArXiv}, year={2013}, volume={abs/1308.3520} }

A Fixed-Parameter Tractable (FPT) ρ-approximation algorithm for a minimization (resp. maximization) parameterized problem P is an FPT algorithm that, given an instance (x, k) ∈ P computes a solution of cost at most k ·ρ(k) (resp. k/ρ(k)) if a solution of cost at most (resp. at least) k exists; otherwise the output can be arbitrary. For well-known intractable problems such as the W[1]-hard Clique and W[2]-hard Set Cover problems, the natural question is whether we can get any FPT-approximation…

## 51 Citations

Fixed parameter approximability and inapproximability

- Computer Science
- 2014

In parameterized complexity the input is refined to (I, k) with k a parameter depending on the input and the goal is to find an exact algorithm that runs in time f(k) ·nO(1) for the problem so that f is an arbitrary function.

Almost Polynomial Factor Inapproximability for Parameterized k-Clique

- Mathematics, Computer ScienceCCC
- 2022

This paper improves the inapproximability result to rule out every F ( k ) = k 1 /H ( k ), factor FPT-approximation algorithm for any increasing computable function H (for example H ( k) = log ∗ k ).

Using the PCP to prove fixed parameter hardness

- Mathematics
- 2017

For a minimization (resp, maximization) problem P , and a parameter k, an algorithm is called a (r(k), t(k))-FPT-approximation algorithm, if for an instance I of size n with optimum opt, the…

Fixed-Parameter Approximability and Hardness

- MathematicsEncyclopedia of Algorithms
- 2016

This survey parameterizes NP-hard problems by the optimum value of the instance unless stated otherwise, and finds that the optimum is always integral.

Fixed parameter inapproximability for Clique and Set-Cover with super exponential time in k

- Mathematics
- 2014

A minimization (resp., maximization) problem is called fixed parameter (r, t)-hard for two r, t if there does not exist an algorithm that given a problem instance I with optimum value opt and an…

A rigorous paradigm for proving Fixed Parameter Inapproximability via gap reductions

- Mathematics
- 2015

For a parameter k, a minimization (resp., maximization) problem is called fixed parameter (r(k), t(k))-hard for two functions r, t if there does not exist an algorithm that given a problem instance I…

On the parameterized complexity of approximating dominating set

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2017

To prove hardness of approximation of a certain parameterized variant of the label cover problem, it suffices to devise a specific protocol for a communication problem that depends on which hypothesis the authors rely on, generalizing the ideas from a recent breakthrough work of Abboud et al.

On the Parameterized Complexity of Approximating Dominating Set

- Computer Science, MathematicsJ. ACM
- 2019

The non-existence of an F(k)-FPT-approximation algorithm for any function F was shown under Gap-ETH and to prove hardness of approximation of a certain parameterized variant of the label cover problem, it suffices to devise a specific protocol for a communication problem that depends on which hypothesis the authors rely on.

On Parameterized Inapproximability of Several Optimization Problems

- Mathematics
- 2016

In this thesis, we study the parameterized inapproximability of several optimization problems. Approximation algorithms and parameterized complexity are two powerful methods to deal with hard…

Reducing the value of the optimum : FPT inapproximability for Set

- Mathematics
- 2013

In Fixed Parameter Tractability (FPT) theory, we are given a problem with a special parameter k. In this paper we are only interested in k equal the size of the optimum. A FPT algorithm for a problem…

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