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 …

Automating cutting planes is NP-hard

M Göös, S Koroth, I Mertz, T Pitassi - … of the 52nd Annual ACM SIGACT …, 2020 - dl.acm.org
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It
is-hard to find a CP refutation of F in time polynomial in the length of the shortest such …

Constant approximating k-clique is w [1]-hard

B Lin - Proceedings of the 53rd Annual ACM SIGACT …, 2021 - dl.acm.org
For every graph G, let ω (G) be the largest size of complete subgraph in G. This paper
presents a simple algorithm which, on input a graph G, a positive integer k and a small …

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 …

Baby pih: Parameterized inapproximability of min csp

V Guruswami, X Ren, S Sandeep - arXiv preprint arXiv:2310.16344, 2023 - arxiv.org
The Parameterized Inapproximability Hypothesis (PIH) is the analog of the PCP theorem in
the world of parameterized complexity. It asserts that no FPT algorithm can distinguish a …

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 …