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Related papers: Distributed domination on sparse graph classes

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We show how to compute a 20-approximation of a minimum dominating set in a planar graph in a constant number of rounds in the LOCAL model of distributed computing. This improves on the previously best known approximation factor of 52, which…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-11-30 Ozan Heydt , Sebastian Siebertz , Alexandre Vigny

We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al.…

Data Structures and Algorithms · Computer Science 2021-06-29 Simeon Kublenz , Sebastian Siebertz , Alexandre Vigny

We provide a new constant factor approximation algorithm for the (connected) distance-$r$ dominating set problem on graph classes of bounded expansion. Classes of bounded expansion include many familiar classes of sparse graphs such as…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-08 Saeed Akhoondian Amiri , Patrice Ossona de Mendez , Roman Rabinovich , Sebastian Siebertz

The Minimum Dominating Set (MDS) problem is not only one of the most fundamental problems in distributed computing, it is also one of the most challenging ones. While it is well-known that minimum dominating sets cannot be approximated…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-02-15 Saeed Akhoondian Amiri , Stefan Schmid , Sebastian Siebertz

The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-04-18 Saeed Akhoondian Amiri , Stefan Schmid , Sebastian Siebertz

We prove that a simple distributed algorithm finds a constant approximation of an optimal distance-$k$ dominating set in graphs with no $K_{2,t}$-minor. The algorithm runs in a constant number of rounds. We further show how this procedure…

Data Structures and Algorithms · Computer Science 2022-03-08 Andrzej Czygrinow , Michał Hanćkowiak , Marcin Witkowski

The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-08 Saeed Akhoondian Amiri , Ben Wiederhake

The k-domination number of a graph is the minimum size of a set X such that every vertex of G is in distance at most k from X. We give a linear time constant-factor approximation algorithm for k-domination number in classes of graphs with…

Combinatorics · Mathematics 2011-10-25 Zdenek Dvorak

We show that graphs excluding $K_{2,t}$ as a minor admit a $f(t)$-round $50$-approximation deterministic distributed algorithm for Minimum Dominating Set. The result extends to Minimum Vertex Cover. Though fast and approximate distributed…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-05-14 Marthe Bonamy , Cyril Gavoille , Timothé Picavet , Alexandra Wesolek

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on…

Data Structures and Algorithms · Computer Science 2011-08-24 Mong-Jen Kao , D. T. Lee

In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-12-24 Mika Göös , Juho Hirvonen , Jukka Suomela

The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…

Data Structures and Algorithms · Computer Science 2018-11-20 Wojciech Nadara

We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-11-22 Marthe Bonamy , Linda Cook , Carla Groenland , Alexandra Wesolek

In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-01-05 Sharareh Alipour , Ehsan Futuhi , Shayan Karimi

We prove that given any $\alpha$-approximation LOCAL algorithm for Minimum Dominating Set (MDS) on planar graphs, we can construct an $f(g)$-round $(3\alpha+1)$-approximation LOCAL algorithm for MDS on graphs embeddable in a given Euler…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-20 Marthe Bonamy , Avinandan Das , Cyril Gavoille , Timothé Picavet , Jukka Suomela , Alexandra Wesolek

The study of domination in graphs has led to a variety of domination problems studied in the literature. Most of these follow the following general framework: Given a graph $G$ and an integer $k$, decide if there is a set $S$ of $k$…

Data Structures and Algorithms · Computer Science 2024-09-13 Marvin Künnemann , Mirza Redzic

Capacitated Domination generalizes the classic Dominating Set problem by specifying for each vertex a required demand and an available capacity for covering demand in its closed neighborhood. The objective is to find a minimum-sized set of…

Data Structures and Algorithms · Computer Science 2016-04-19 Amariah Becker

This paper presents a distributed algorithm for finding near optimal dominating sets on grids. The basis for this algorithm is an existing centralized algorithm that constructs dominating sets on grids. The size of the dominating set…

Data Structures and Algorithms · Computer Science 2013-03-15 Elaheh Fata , Stephen L. Smith , Shreyas Sundaram

We give a new, short proof that graphs embeddable in a given Euler genus-$g$ surface admit a simple $f(g)$-round $\alpha$-approximation distributed algorithm for Minimum Dominating Set (MDS), where the approximation ratio $\alpha \le 906$.…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-07-08 Marthe Bonamy , Cyril Gavoille , Timothé Picavet , Alexandra Wesolek

We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a $(7-\epsilon)$-approximation of a minimum dominating set on planar graphs, for any positive constant $\epsilon$. In prior work,…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-02-12 Miikka Hilke , Christoph Lenzen , Jukka Suomela
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