Tight Complexity Bounds for Counting Generalized Dominating Sets in Bounded-Treewidth Graphs Part II: Hardness Results

J Focke, D Marx, F Mc Inerney, D Neuen… - ACM Transactions on …, 2024 - dl.acm.org
For a well-studied family of domination-type problems, in bounded-treewidth graphs, we
investigate whether it is possible to find faster algorithms. For sets σ, ρ of non-negative …

Parameterized Intractability of Even Set and Shortest<? brk?> Vector Problem

A Bhattacharyya, É Bonnet, L Egri, S Ghoshal… - Journal of the ACM …, 2021 - dl.acm.org
The-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear
codes over, which can be stated as follows: given a generator matrix and an integer …

[HTML][HTML] A width parameter useful for chordal and co-comparability graphs

DY Kang, O Kwon, TJF Strømme, JA Telle - Theoretical Computer Science, 2017 - Elsevier
Belmonte and Vatshelle (TCS 2013) used mim-width, a graph width parameter bounded on
interval graphs and permutation graphs, to explain existing algorithms for many domination …

Parameterized intractability of even set and shortest vector problem from gap-eth

A Bhattacharyya, S Ghoshal, P Manurangsi - arxiv preprint arxiv …, 2018 - arxiv.org
The $ k $-Even Set problem is a parameterized variant of the Minimum Distance Problem of
linear codes over $\mathbb F_2 $, which can be stated as follows: given a generator matrix …

Structurally robust control of complex networks

JC Nacher, T Akutsu - Physical Review E, 2015 - APS
Robust control theory has been successfully applied to numerous real-world problems using
a small set of devices called controllers. However, the real systems represented by networks …

The mixed Chinese postman problem parameterized by pathwidth and treedepth

G Gutin, M Jones, M Wahlstrom - SIAM Journal on Discrete Mathematics, 2016 - SIAM
In the mixed Chinese postman problem (MCPP), given a weighted mixed graph G (it may
have both edges and arcs), our aim is to find a closed walk of minimum weight traversing …

The parameterized complexity of domination-type problems and application to linear codes

D Cattanéo, S Perdrix - … Conference on Theory and Applications of Models …, 2014 - Springer
We study the parameterized complexity of domination-type problems.(σ, ρ)-domination is a
general and unifying framework introduced by Telle: given σ, ρ⊆ ℕ, a set D of vertices of a …

Structural parameterizations of the mixed chinese postman problem

G Gutin, M Jones, M Wahlström - … , Patras, Greece, September 14-16, 2015 …, 2015 - Springer
Abstract In the Mixed Chinese Postman Problem (MCPP), given a weighted mixed graph G
(G may have both edges and arcs), our aim is to find a minimum weight closed walk …

Residue Domination in Bounded-Treewidth Graphs

J Greilhuber, P Schepper… - … Symposium on Theoretical …, 2025 - drops.dagstuhl.de
For the vertex selection problem (σ, ρ)-DomSet one is given two fixed sets σ and ρ of
integers and the task is to decide whether we can select vertices of the input graph such that …

On the hardness of generalized domination problems parameterized by mim-width

BIK Bakkane, L Jaffke - 17th International Symposium on …, 2022 - drops.dagstuhl.de
For nonempty σ, ρ⊆ ℕ, a vertex set S in a graph G is a (σ, ρ)-dominating set if for all v∈ S,| N
(v)∩ S|∈ σ, and for all v∈ V (G)⧵ S,| N (v)∩ S|∈ ρ. The Min/Max (σ, ρ)-Dominating Set …