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 …

Improved hardness of approximating k-clique under ETH

B Lin, X Ren, Y Sun, X Wang - 2023 IEEE 64th Annual …, 2023 - ieeexplore.ieee.org
In this paper, we prove that assuming the exponential time hypothesis (ETH), there is no
f(k)⋅n^k^o(1/\log\logk)-time algorithm that can decide whether an n-vertex graph contains a …

[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 …

Optimally repurposing existing algorithms to obtain exponential-time approximations

B Can Esmer, A Kulik, D Marx, D Neuen… - Proceedings of the 2024 …, 2024 - SIAM
The goal of this paper is to understand how exponential-time approximation algorithms can
be obtained from existing polynomial-time approximation algorithms, existing parameterized …

Simple Combinatorial Construction of the -Lower Bound for Approximating the Parameterized -Clique

Y Chen, Y Feng, B Laekhanukit, Y Liu - arXiv preprint arXiv:2304.07516, 2023 - arxiv.org
In the parameterized $ k $-clique problem, or $ k $-Clique for short, we are given a graph $
G $ and a parameter $ k\ge 1$. The goal is to decide whether there exist $ k $ vertices in $ G …

Parameterized Inapproximability Hypothesis under ETH

V Guruswami, B Lin, X Ren, Y Sun, K Wu - arXiv preprint arXiv:2311.16587, 2023 - arxiv.org
The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter
tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the …

Fast decision tree learning solves hard coding-theoretic problems

C Koch, C Strassle, LY Tan - 2024 IEEE 65th Annual …, 2024 - ieeexplore.ieee.org
We connect the problem of properly PAC learning decision trees to the parameterized
Nearest Codeword Problem (k-NCP). Despite significant effort by the respective …

Parameterized Inapproximability of Independent Set in H-Free Graphs

P Dvořák, AE Feldmann, A Rai, P Rzążewski - Algorithmica, 2023 - Springer
Abstract We study the Independent Set problem in H-free graphs, ie, graphs excluding some
fixed graph H as an induced subgraph. We prove several inapproximability results both for …

Fine Grained Lower Bounds for Multidimensional Knapsack

I Doron-Arad, A Kulik, P Manurangsi - arXiv preprint arXiv:2407.10146, 2024 - arxiv.org
We study the $ d $-dimensional knapsack problem. We are given a set of items, each with a
$ d $-dimensional cost vector and a profit, along with a $ d $-dimensional budget vector. The …