Related papers: Distributed Dominating Sets on Grids
In this paper we study the dynamic versions of two basic graph problems: Minimum Dominating Set and its variant Minimum Connected Dominating Set. For those two problems, we present algorithms that maintain a solution under edge insertions…
Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset $U$ of nodes is a dominating set if each node is either in…
The online dominating set problem is an online variant of the minimum dominating set problem, which is one of the most important NP-hard problems on graphs. This problem is defined as follows: Given an undirected graph $G = (V, E)$, in…
Rule k is a localized approximation algorithm that finds a small connected dominating set in a graph. We estimate the expected size of the Rule k dominating set for the model of random unit disk graphs constructed from n random points in an…
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…
The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting…
A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem…
The domination problem and its variants represent a classical domain within algorithmic graph theory. Among these variants, the paired-domination problem holds particular prominence due to its real-world implications in security and…
This study focusses on self-balancing microgrids to smartly utilize and prevent overdrawing of available power capacity of the grid. A distributed framework for automated distribution of optimal power demand is proposed, where all building…
A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…
Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large…
We study ensemble-based graph-theoretical methods aiming to approximate the size of the minimum dominating set (MDS) in scale-free networks. We analyze both analytical upper bounds of dominating sets and numerical realizations for…
Gathering is a fundamental coordination problem in swarm robotics, where the objective is to bring robots together at a point not known to them at the beginning. While most research focuses on continuous domains, some studies also examine…
A dominating set in a graph $G$ is a subset of vertices $D$ such that every vertex in $V\setminus D$ is a neighbor of some vertex of $D$. The domination number of $G$ is the minimum size of a dominating set of $G$ and it is denoted by…
In this paper, we consider the unconstrained distributed optimization problem, in which the exchange of information in the network is captured by a directed graph topology, thus, nodes can only communicate with their neighbors.…
Assuming a random uniform distribution of n sensor nodes over a virtual grid, this paper addresses the problem of finding the maximum number of connected set covers each ensuring 100% coverage of the query region. The connected sets remain…
In his 1992 Ph.D. thesis Chang identified an efficient way to dominate $m \times n$ grid graphs and conjectured that his construction gives the most efficient dominating sets for relatively large grids. In 2011 Gon\c{c}alves, Pinlou, Rao,…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
We consider a minimizing variant of the well-known \emph{No-Three-In-Line Problem}, the \emph{Geometric Dominating Set Problem}: What is the smallest number of points in an $n\times n$~grid such that every grid point lies on a common line…
Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its…