Related papers: Weak dynamic monopolies in social graphs

Let $G$ be a graph and ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be dynamic monopoly (or simply dynamo) if the vertices of $G$ can be partitioned…

Let $G$ be a graph and ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}\cup \{0\}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be a dynamic monopoly corresponding to $(G, \tau)$ if the vertices of…

Let $G$ be a directed graph such that the in-degree of any vertex $G$ is at least one. Let also ${\mathcal{\tau}}: V(G)\rightarrow \Bbb{N}$ be an assignment of thresholds to the vertices of $G$. A subset $M$ of vertices of $G$ is called a…

Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…

For a graph $G$ and an integer-valued threshold function $\tau$ on its vertex set, a dynamic monopoly is a set of vertices of $G$ such that iteratively adding to it vertices $u$ of $G$ that have at least $\tau(u)$ neighbors in it eventually…

We address the problem of computing a Minimal Dominating Set in highly dynamic distributed systems. We assume weak connectivity, i.e., the network may be disconnected at each time instant and topological changes are unpredictable. We make…

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The…

Let $G$ be a graph and $\tau$ be an assignment of nonnegative integer thresholds to the vertices of $G$. Denote the average of thresholds in $\tau$ by $\bar{\tau}$. A subset of vertices $D$ is said to be a $\tau$-dynamic monopoly, if $V(G)$…

A graph $G$ is said to be a $k$-degenerate graph if any subgraph of $G$ contains a vertex of degree at most $k$. Let $\kappa$ be any non-negative function on the vertex set of $G$. We first define a $\kappa$-degenerate graph. Next we give…

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…

A widely studied model for influence diffusion in social networks are {\it target sets}. For a graph $G$ and an integer-valued threshold function $\tau$ on its vertex set, a {\it target set} or {\it dynamic monopoly} is a set of vertices of…

A widely studied process of influence diffusion in social networks posits that the dynamics of influence diffusion evolves as follows: Given a graph $G=(V,E)$, representing the network, initially \emph{only} the members of a given…

The spread of influence in social networks is studied in two main categories: the progressive model and the non-progressive model (see e.g. the seminal work of Kempe, Kleinberg, and Tardos in KDD 2003). While the progressive models are…

In this work, we study the propagation of influence and computation in dynamic distributed systems. We focus on broadcasting models under a worst-case dynamicity assumption which have received much attention recently. We drop for the first…

For a graph $G$ and an integer-valued function $\tau$ on its vertex set, a dynamic monopoly is a set of vertices of $G$ such that iteratively adding to it vertices $u$ of $G$ that have at least $\tau(u)$ neighbors in it eventually yields…

Let $G$ be any simple and undirected graph. By a threshold assignment $\tau$ in $G$ we mean any function $\tau:V(G)\rightarrow \mathbb{N}$ such that $\tau(v)\leq d_G(v)$ for any vertex $v$ of $G$. Given a graph $G$ with a threshold…

Let $G$ be a graph and $\tau$ be an assignment of nonnegative integer thresholds to the vertices of $G$. A subset of vertices $D$ is said to be a $\tau$-dynamic monopoly, if $V(G)$ can be partitioned into subsets $D_0, D_1, \ldots, D_k$…

Given a network represented by a graph $G=(V,E)$, we consider a dynamical process of influence diffusion in $G$ that evolves as follows: Initially only the nodes of a given $S\subseteq V$ are influenced; subsequently, at each round, the set…

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their…

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics,…