Computing tree decompositions with small independence number
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 …
numbers of the subgraphs induced by its bags. The tree-independence number of a graph is …
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 …
Improved hardness of approximating k-clique under ETH
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 …
f(k)⋅n^k^o(1/\log\logk)-time algorithm that can decide whether an n-vertex graph contains a …
On Lower Bounds of Approximating Parameterized -Clique
Given a simple graph $ G $ and an integer $ k $, the goal of $ k $-Clique problem is to
decide if $ G $ contains a complete subgraph of size $ k $. We say an algorithm …
decide if $ G $ contains a complete subgraph of size $ k $. We say an algorithm …
[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 …
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 …
G $ and a parameter $ k\ge 1$. The goal is to decide whether there exist $ k $ vertices in $ G …
Parameterized Inapproximability Hypothesis under ETH
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 …
Parameterized Complexity of Equality MinCSP
G Osipov, M Wahlström - arXiv preprint arXiv:2305.11131, 2023 - arxiv.org
We study the parameterized complexity of MinCSP for so-called equality languages, ie, for
finite languages over an infinite domain such as $\mathbb {N} $, where the relations are …
finite languages over an infinite domain such as $\mathbb {N} $, where the relations are …
On Equivalence of Parameterized Inapproximability of k-Median, k-Max-Coverage, and 2-CSP
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 …
of parameterized complexity. PIH asserts that given as input a 2-CSP on k variables and …
Constant Approximating Disjoint Paths on Acyclic Digraphs Is W [1]-Hard
M Włodarczyk - arXiv preprint arXiv:2409.03596, 2024 - arxiv.org
In the Disjoint Paths problem, one is given a graph with a set of $ k $ vertex pairs $(s_i, t_i) $
and the task is to connect each $ s_i $ to $ t_i $ with a path, so that the $ k $ paths are …
and the task is to connect each $ s_i $ to $ t_i $ with a path, so that the $ k $ paths are …