Related papers: Approximability of the Minimum Weighted Doubly Res…
Given a connected graph $G$ with at least three vertices, let $d_G(u,v)$ denote the distance between vertices $u,v\in V(G)$. A subset $S\subseteq V$ is called a doubly resolving set (DRS) of $G$ if for any two distinct vertices $u, v \in…
Given a graph, the minimum dominating set (MinDS) problem is to identify a smallest set $D$ of vertices such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The MinDS problem is a classic $\mathcal{NP}$-hard problem…
In this paper, we study the minimum dominating set (MDS) problem and the minimum total dominating set MTDS) problem which have many applications in real world. We propose a new idea to compute approximate MDS and MTDS. Next, we give an…
Source localization in graphs involves identifying the origin of a phenomenon or event, such as an epidemic outbreak or a misinformation source, by leveraging structural graph properties. One key concept in this context is the metric…
Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is…
We consider the minimum weight and smallest weight minimum-size dominating set problems in vertex-weighted graphs and networks. The latter problem is a two-objective optimization problem, which is different from the classic minimum weight…
Given a set $S$ of points in the plane, a geometric network for $S$ is a graph $G$ with vertex set $S$ and straight edges. We consider a broadcasting situation, where one point $r \in S$ is a designated source. Given a dilation factor…
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…
In the minimum $k$-edge-connected spanning subgraph ($k$-ECSS) problem the goal is to find the minimum weight subgraph resistant to up to $k-1$ edge failures. This is a central problem in network design, and a natural generalization of the…
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes $S$ that power dominates all the nodes, where a node $v$ is power dominated if (1) $v$ is in $S$…
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…
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…
The minimum-weight $2$-edge-connected spanning subgraph (2-ECSS) problem is a natural generalization of the well-studied minimum-weight spanning tree (MST) problem, and it has received considerable attention in the area of network design.…
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
Information diffusion in networks can be used to model many real-world phenomena, including rumor spreading on online social networks, epidemics in human beings, and malware on the Internet. Informally speaking, the source localization…
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…
Consider~\(n\) nodes~\(\{X_i\}_{1 \leq i \leq n}\) independently distributed in the unit square~\(S,\) each according to a distribution~\(f.\) Nodes~\(X_i\) and~\(X_j\) are joined by an edge if the Euclidean distance~\(d(X_i,X_j)\) is less…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
In this paper, we give approximation algorithms for the \textsc{Minimum Dominating Set (MDS)} problem on \emph{string} graphs and its subclasses. A \emph{path} is a simple curve made up of alternating horizontal and vertical line segments.…
We consider the k-outconnected directed Steiner tree problem (k-DST). Given a directed edge-weighted graph $G=(V,E,w)$, where $V=\{r\}\cup S \cup T$, and an integer $k$, the goal is to find a minimum cost subgraph of $G$ in which there are…