A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

TL;DR

This survey reviews recent advances in combining parameterization and approximation techniques to address NP-hard problems, highlighting new methods, hardness results, and future research directions.

Contribution

It provides a comprehensive overview of the intersection of parameterized complexity and approximation algorithms, emphasizing recent developments and open problems.

Findings

New techniques in parameterized approximation algorithms

Hardness results for approximation in parameterized settings

Potential future research directions in the field

Abstract

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and hardness perspectives, with emphasis on new techniques and potential future research directions.