A survey on approximation in parameterized complexity: Hardness and algorithms
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 …
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 …
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
Over the past decade, many results have focused on the design of parameterized
approximation algorithms for W [1]-hard problems. However, there are fundamental …
approximation algorithms for W [1]-hard problems. However, there are fundamental …
Automating cutting planes is NP-hard
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 …
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 …
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 …
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 …
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 …
the world of parameterized complexity. It asserts that no FPT algorithm can distinguish a …
Constant Approximating Parameterized k-SETCOVER is W[2]-hard
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 …
ratio. Our proof is built upon the recently developed threshold graph composition technique …
[PDF][PDF] Parameterized Inapproximability Hypothesis under Exponential Time Hypothesis
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter
tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the …
tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the …