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The problem of finding a minimum-weight connected dominating set (CDS) of a given undirected graph has been studied actively, motivated by operations of wireless ad hoc networks. In this paper, we formulate a new stochastic variant of the…

Data Structures and Algorithms · Computer Science 2020-01-01 Takuro Fukunaga

The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given simple graph $G=(V,E)$, a dominating set of $G$ is a subset $S\subseteq V$ such that every vertex in $…

Combinatorics · Mathematics 2022-11-01 Nima Ghanbari , Gerold Jäger , Tuomo Lehtilä

Dominating set problems are among the most important class of combinatorial problems in graph optimization, from a theoretical as well as from a practical point of view. In this paper, we address the recently introduced (minimum) weighted…

Optimization and Control · Mathematics 2019-10-09 Eduardo Álvarez-Miranda , Markus Sinnl

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

Priebe et al. (2001) introduced the class cover catch digraphs and computed the distribution of the domination number of such digraphs for one dimensional data. In higher dimensions these calculations are extremely difficult due to the…

Methodology · Statistics 2008-02-06 E. Ceyhan , C. E. Priebe

A mixed dominating set of a graph $G = (V, E)$ is a mixed set $D$ of vertices and edges, such that for every edge or vertex, if it is not in $D$, then it is adjacent or incident to at least one vertex or edge in $D$. The mixed domination…

Data Structures and Algorithms · Computer Science 2019-06-27 Mingyu Xiao

A connected dominating set is a widely adopted model for the virtual backbone of a wireless sensor network. In this paper, we design an evolutionary algorithm for the minimum connected dominating set problem (MinCDS), whose performance is…

Discrete Mathematics · Computer Science 2022-01-17 Chaojie Zhu , Yingli Ran , Zhao Zhang , Ding-Zhu Du

A mixed dominating set for a graph $G = (V,E)$ is a set $S\subseteq V \cup E$ such that every element $x \in (V \cup E) \backslash S$ is either adjacent or incident to an element of $S$. The mixed domination number of a graph $G$, denoted…

Discrete Mathematics · Computer Science 2023-06-22 M. Rajaati , M. R. Hooshmandasl , M. J. Dinneen , A. Shakiba

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

Efficient communication between nodes in ad-hoc networks can be established through repeated cluster formations with designated \textit{cluster-heads}. In this context minimum d-hop dominating set problem was introduced for cluster…

Data Structures and Algorithms · Computer Science 2017-01-27 Joydeep Banerjee , Arun Das , Arunabha Sen

The question to enumerate all inclusion-minimal connected dominating sets in a graph of order $n$ in time significantly less than $2^n$ is an open question that was asked in many places. We answer this question affirmatively, by providing…

Computational Complexity · Computer Science 2022-05-03 Faisal Abu-Khzam , Henning Fernau , Benjamin Gras , Mathieu Liedloff , Kevin Mann

We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-03-20 Martin Biely , Peter Robinson , Ulrich Schmid

The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is…

Combinatorics · Mathematics 2025-12-15 Misa Nakanishi

A minimum dominating set in a graph is a minimum set of vertices such that every vertex of the graph either belongs to it, or is adjacent to one vertex of this set. This mathematical object is of high relevance in a number of applications…

Artificial Intelligence · Computer Science 2018-08-30 Mayra Albuquerque , Thibaut Vidal

In this paper, we study the dominating set problem in \emph{RDV graphs}, a graph class that lies between interval graphs and chordal graphs and is defined as the \textbf{v}ertex-intersection graphs of \textbf{d}ownward paths in a…

Data Structures and Algorithms · Computer Science 2026-01-09 Therese Biedl , Prashant Gokhale

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

Conventional spectral digraph partitioning methods typically symmetrize the adjacency matrix, thereby transforming the directed graph partitioning problem into an undirected one, where bipartitioning is commonly linked to minimizing graph…

Optimization and Control · Mathematics 2025-07-01 Sihong Shao , Chuan Yang , Xinyang Ye

Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in…

Combinatorics · Mathematics 2017-11-15 Chassidy Bozeman , Boris Brimkov , Craig Erickson , Daniela Ferrero , Mary Flagg , Leslie Hogben

We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge…

Statistical Mechanics · Physics 2009-11-13 M. Mézard , M. Tarzia

A set $D \subseteq V$ for the graph $G=(V, E)$ is called a dominating set if any vertex $v\in V\setminus D$ has at least one neighbor in $D$. Fomin et al.[9] gave an algorithm for enumerating all minimal dominating sets with $n$ vertices in…

Discrete Mathematics · Computer Science 2018-06-08 M. Alambardar Meybodi , M. R. Hooshmandasl , P. Sharifani , A. Shakiba