A Survey on Parameterized Inapproximability: $k$-Clique, $k$-SetCover, and More

TL;DR

This survey reviews recent parameterized inapproximability results for problems like k-Clique and k-SetCover, highlighting advances in understanding their computational hardness.

Contribution

It compiles and analyzes recent inapproximability findings from the parameterized complexity perspective for key combinatorial problems.

Findings

Many problems remain hard to approximate within certain bounds

Recent results establish tight inapproximability thresholds

The survey identifies open challenges in parameterized inapproximability

Abstract

In the past a few years, many interesting inapproximability results have been obtained from the parameterized perspective. This article surveys some of such results, with a focus on $k$-Clique, $k$-SetCover, and other related problems.