[PDF][PDF] Various properties of various ultrafilters, various graph width parameters, and various connectivity systems

T Fujita - arXiv preprint arXiv, 2024 - researchgate.net
This paper investigates ultrafilters in the context of connectivity systems, defined as pairs (X,
f) where X is a finite set and f is a symmetric submodular function. Ultrafilters, essential in …

A Short Review on Novel Approaches for Maximum Clique Problem: from Classical algorithms to Graph Neural Networks and Quantum algorithms

R Marino, L Buffoni, B Zavalnij - arXiv preprint arXiv:2403.09742, 2024 - arxiv.org
This manuscript provides a comprehensive review of the Maximum Clique Problem, a
computational problem that involves finding subsets of vertices in a graph that are all …

Parameterized analysis and crossing minimization problems

M Zehavi - Computer Science Review, 2022 - Elsevier
In this survey/introductory article, we first present the basics of the field of Parameterized
Complexity, made accessible to readers without background on the subject. Afterwards, we …

Computing tree decompositions with small independence number

C Dallard, FV Fomin, PA Golovach, T Korhonen… - arXiv preprint arXiv …, 2022 - arxiv.org
The independence number of a tree decomposition is the maximum of the independence
numbers of the subgraphs induced by its bags. The tree-independence number of a graph is …

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 …

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 …

Planar disjoint paths, treewidth, and kernels

M Włodarczyk, M Zehavi - 2023 IEEE 64th Annual Symposium …, 2023 - ieeexplore.ieee.org
In the PLANAR DISJOINT PATHS problem, one is given an undirected planar graph with a
set of k vertex pairs \left(s_i,t_i\right) and the task is to find k pairwise vertex-disjoint paths …

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 …

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 …