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 …

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 …

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 …

Superpolynomial lower bounds for decision tree learning and testing

C Koch, C Strassle, LY Tan - Proceedings of the 2023 Annual ACM-SIAM …, 2023 - SIAM
We establish new hardness results for decision tree optimization problems, adding to a line
of work that dates back to Hyafil and Rivest in 1976. We prove, under the randomized …

Applications of random algebraic constructions to hardness of approximation

B Bukh, CS Karthik, B Narayanan - 2021 IEEE 62nd Annual …, 2022 - ieeexplore.ieee.org
In this paper, we show how one may (efficiently) construct two types of extremal
combinatorial objects whose existence was previously conjectural.• Panchromatic Graphs …

On Equivalence of Parameterized Inapproximability of k-Median, k-Max-Coverage, and 2-CSP

CS Karthik, E Lee, P Manurangsi - 19th International Symposium …, 2024 - drops.dagstuhl.de
Abstract Parameterized Inapproximability Hypothesis (PIH) is a central question in the field
of parameterized complexity. PIH asserts that given as input a 2-CSP on k variables and …

Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems under ETH

S Li, B Lin, Y Liu - arXiv preprint arXiv:2402.09825, 2024 - arxiv.org
In this paper we present a new gap-creating randomized self-reduction for parameterized
Maximum Likelihood Decoding problem over $\mathbb {F} _p $($ k $-MLD $ _p $). The …