Related papers: Weighted domination models and randomized heuristi…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
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…
For a given graph $G = (V, E)$, a subset of the vertices $D\subseteq V$ is called a semitotal dominating set, if $D$ is a dominating set and every vertex $v \in D$ is within distance two to another witness $v' \in D$. We want to find a…
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 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…
Covering problems are classical computational problems concerning whether a certain combinatorial structure 'covers' another. For example, the minimum vertex covering problem aims to find the smallest set of vertices in a graph so that each…
The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to…
Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and…
We investigate the problem of simultaneously dominating all spanning trees of a given graph. We prove that on 2-connected graphs, a subset of the vertices dominates all spanning trees of the graph if and only if it is a vertex cover. Using…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
Given a graph $G=(V,E)$, a vertex $u \in V$ {\em ve-dominates} all edges incident to any vertex of $N_G[u]$. A set $S \subseteq V$ is a {\em ve-dominating set} if for all edges $e\in E$, there exists a vertex $u\in S$ such that $u$…
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…
Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…
We present a novel neural architecture to solve graph optimization problems where the solution consists of arbitrary node labels, allowing us to solve hard problems like graph coloring. We train our model using reinforcement learning,…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
In this paper, we consider distributed optimization design for resource allocation problems over weight-balanced graphs. With the help of singular perturbation analysis, we propose a simple sub-optimal continuous-time optimization…
In a graph $G$, a vertex subset $S\subseteq V(G)$ is said to be a dominating set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A dominating set $S$ of a graph $G$ is called a paired-dominating set if the induced subgraph…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
Given a graph $G=(V,E)$ and an integer $k$, the Minimum Membership Dominating Set (MMDS) problem seeks to find a dominating set $S \subseteq V$ of $G$ such that for each $v \in V$, $|N[v] \cap S|$ is at most $k$. We investigate the…