Related papers: On distributed algorithms for minimum dominating s…
We consider the problem of selecting a minimum size subset of nodes in a network, that allows to activate all the nodes of the network. We present a fast and simple algorithm that, in real-life networks, produces solutions that outperform…
Let $G = (V,E)$ be a simple, undirected and connected graph. A connected dominating set $S \subseteq V$ is a secure connected dominating set of $G$, if for each $ u \in V\setminus S$, there exists $v\in S$ such that $(u,v) \in E$ and the…
Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and…
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…
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.…
We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. We focus on the well known minimum degree greedy…
A dominating set $D$ of a graph $G$ is a set of vertices such that any vertex in $G$ is in $D$ or its neighbor is in $D$. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of…
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…
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…
We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank $f$. This problem is equivalent to the Minimum Weight Set Cover Problem in which the frequency of every…
A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find $r$-dominating sets which enable…
We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size $N$ and power-law exponent $\gamma$, while keeping the average degree fixed. We study ensembles generated by…
We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The…
We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…
The dominating set problem has many practical applications but is well-known to be NP-hard. Therefore, there is a need for efficient approximation algorithms, especially in applications such as ad hoc wireless networks. Most distributed…
In this article, we study a variant of the minimum dominating set problem known as the minimum liar's dominating set (MLDS) problem. We prove that the MLDS problem is NP-hard in unit disk graphs. Next, we show that the recent sub-quadratic…
In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree…
Dominating Set is a well-known combinatorial optimization problem which finds application in computational biology or mobile communication. Because of its $\mathrm{NP}$-hardness, one often turns to heuristics for good solutions. Many such…
Consider a graph with nonnegative node weight. A vertex subset is called a CDS (connected dominating set) if every other node has at least one neighbor in the subset and the subset induces a connected subgraph. Furthermore, if every other…
Given a positive integer $k$, a $k$-dominating set in a graph $G$ is a set of vertices such that every vertex not in the set has at least $k$ neighbors in the set. A total $k$-dominating set, also known as a $k$-tuple total dominating set,…