A survey on approximation in parameterized complexity: Hardness and algorithms

AE Feldmann, E Lee, P Manurangsi - Algorithms, 2020 - mdpi.com
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 …

Tight Running Time Lower Bounds for Strong Inapproximability of Maximum k-Coverage, Unique Set Cover and Related Problems (via t-Wise Agreement Testing …

P Manurangsi - Proceedings of the Fourteenth Annual ACM-SIAM …, 2020 - SIAM
We show, assuming the (randomized) Gap Exponential Time Hypothesis (Gap-ETH), that
the following tasks cannot be done in T (k)· N o (k)-time for any function T where N denote …

FPT-approximation for FPT problems

D Lokshtanov, P Misra, MS Ramanujan… - Proceedings of the 2021 …, 2021 - SIAM
Over the past decade, many results have focused on the design of parameterized
approximation algorithms for W [1]-hard problems. However, there are fundamental …

The complexity of adversarially robust proper learning of halfspaces with agnostic noise

I Diakonikolas, DM Kane… - Advances in Neural …, 2020 - proceedings.neurips.cc
We study the computational complexity of adversarially robust proper learning of halfspaces
in the distribution-independent agnostic PAC model, with a focus on $ L_p $ perturbations …

Almost polynomial factor inapproximability for parameterized k-clique

CS Karthik, S Khot - 37th Computational Complexity Conference …, 2022 - drops.dagstuhl.de
The k-Clique problem is a canonical hard problem in parameterized complexity. In this
paper, we study the parameterized complexity of approximating the k-Clique problem where …

Parameterized Inapproximability of the Minimum Distance Problem over All Fields and the Shortest Vector Problem in All ℓp Norms

H Bennett, M Cheraghchi, V Guruswami… - Proceedings of the 55th …, 2023 - dl.acm.org
We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite
field and parameterized by the input distance bound is W [1]-hard to approximate within any …

The complexity of the shortest vector problem

H Bennett - ACM SIGACT News, 2023 - dl.acm.org
Computational problems on point lattices play a central role in many areas of computer
science including integer programming, coding theory, cryptanalysis, and especially the …

Constant Approximating Parameterized k-SETCOVER is W[2]-hard

B Lin, X Ren, Y Sun, X Wang - Proceedings of the 2023 Annual ACM-SIAM …, 2023 - SIAM
In this paper, we prove that it is W [2]-hard to approximate k-SETCOVER within any constant
ratio. Our proof is built upon the recently developed threshold graph composition technique …

[PDF][PDF] Parameterized Inapproximability Hypothesis under Exponential Time Hypothesis

V Guruswami, B Lin, X Ren, Y Sun, K Wu - Proceedings of the 56th …, 2024 - dl.acm.org
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter
tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the …

Hardness of the (approximate) shortest vector problem: A simple proof via reed-solomon codes

H Bennett, C Peikert - arXiv preprint arXiv:2202.07736, 2022 - arxiv.org
$\newcommand {\NP}{\mathsf {NP}}\newcommand {\GapSVP}{\textrm {GapSVP}} $ We give
a simple proof that the (approximate, decisional) Shortest Vector Problem is $\NP $-hard …