Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1802.09801

Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-Wideness

Wojciech Nadara·Marcin Pilipczuk·Roman Rabinovich·Felix Reidl·Sebastian Siebertz
View original source ↗Read source document ↗Export metadata ↓

Abstract

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we study two structural properties of these graph classes that are of particular importance in this context, namely the property of having bounded generalized coloring numbers and the property of being uniformly quasi-wide. We provide experimental evaluations of several algorithms that approximate these parameters on real-world graphs. On the theoretical side, we provide a new algorithm for uniform quasi-wideness with polynomial size guarantees in graph classes of bounded expansion and show a lower bound indicating that the guarantees of this algorithm are close to optimal in graph classes with fixed excluded minor.

Explore related subjects

cs.DM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Wojciech Nadara, Marcin Pilipczuk, Roman Rabinovich, Felix Reidl, Sebastian Siebertz. 2019-09-24. Empirical Evaluation of Approximation Algorithms for Generalized Graph Coloring and Uniform Quasi-Wideness. https://arxiv.org/abs/1802.09801

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Factorisability of Low Dimensional Non-Negative Integer Matrices

We consider the problem of determining if a given two-dimensional nonnegative integer matrix $M$ is the product of two such matrices, excluding trivial units. A matrix $M$ with no such factorisation is called prime and therefore belongs to the minimal (infinite rank) generator of $2 \times 2$ matrices over the natural numbers, otherwise it is called composite. We also consider the problem of finding a (non-unique) factorisation of a composite matrix. Our results have applications in computational group theory and the theory of codes, where such matrices are called incidence matrices. We analyse the complexity of primality and finding a factorisation for a composite matrix, providing a first efficient algorithm.

cs.DM↗
arXiv2026

The parameterised complexity of generalised temporal domination on temporal graphs with modular structure

Inspired by the static problem $(α,β)$-Dominating Set, we propose a general temporal domination problem, called $(α,β)$-Temporal Dominating Set ($(α,β)$-TDS). We show that this problem encompasses Temporal Dominating Set, and additionally provides first temporal extensions of problems such as $k$-Dominating Set and $α$-Dominating Set. In this paper, we study the parameterised complexity of $(α,β)$-TDS with respect to temporal neighbourhood diversity (TND), temporal modular-width (TMW), and temporal cliquewidth (TCW). We obtain fixed parameter tractability results for all values of $α$ and $β$ with respect to TND; W[1]-hardness with respect to TMW and TCW whenever $β$ is in the problem input, or whenever $α\in (0,1)$ and $β$ is a fixed constant; and para-NP-hardness with respect to TCW when $α= 0$ and $β= 1$, or $α= 1$ and $β= 0$.

cs.DM↗