Related papers: Asymptotics for Push on the Complete Graph
Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a…
We consider allcast and multicast flow problems where either all of the nodes or only a subset of the nodes may be in session. Traffic from each node in the session has to be sent to every other node in the session. If the session does not…
In this paper, we consider a random network such that there could be a link between any two nodes in the network with a certain probability (plink). Diffusion is the phenomenon of spreading information throughout the network, starting from…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We describe a protocol for the average consensus problem on any fixed undirected graph whose convergence time scales linearly in the total number nodes $n$. The protocol is completely distributed, with the exception of requiring all nodes…
This paper revisits the study of (minimum) broadcast graphs, i.e., graphs enabling fast information dissemination from every source node to all the other nodes (and having minimum number of edges for this property). This study is performed…
We analyze a class of distributed quantized consensus algorithms for arbitrary static networks. In the initial setting, each node in the network has an integer value. Nodes exchange their current estimate of the mean value in the network,…
Let $G = (V,E)$ be a connected directed graph on $n$ vertices. Assign values from the set $\{1,2,\dots,n\}$ to the vertices of $G$ and update the values according to the following rule: uniformly at random choose a vertex and update its…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
We study randomized gossip-based processes in dynamic networks that are motivated by discovery processes in large-scale distributed networks like peer-to-peer or social networks. A well-studied problem in peer-to-peer networks is the…
We consider the problem of detecting the source of a rumor which has spread in a network using only observations about which set of nodes are infected with the rumor and with no information as to \emph{when} these nodes became infected. In…
Consider that $u_0$ nodes are aware of some piece of data $d_0$. This note derives the expected time required for the data $d_0$ to be disseminated through-out a network of $n$ nodes, when communication between nodes evolves according to a…
Broadcasting and convergecasting are pivotal services in distributed systems, in particular, in wireless ad-hoc and sensor networks, which are characterized by time- varying communication graphs. We study the question of whether it is…
A nonsplit graph is a directed graph where each pair of nodes has a common incoming neighbor. We show that the radius of such graphs is in $O(\log \log n)$, where $n$ is the number of nodes. We then generalize the result to products of…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…
This paper investigates the dissemination of multiple pieces of information in large networks where users contact each other in a random uncoordinated manner, and users upload one piece per unit time. The underlying motivation is the design…
Given a network and a set of vertices called seeds to initially inject information, influence spread is the expected number of vertices that eventually receive the information under a certain stochastic model of information propagation.…
We consider \emph{plurality consensus} in a network of $n$ nodes. Initially, each node has one of $k$ opinions. The nodes execute a (randomized) distributed protocol to agree on the plurality opinion (the opinion initially supported by the…
We study the problem of maintaining robust and sparse overlay networks in fully distributed settings where nodes continuously join and leave the system. This scenario closely models real-world unstructured peer-to-peer networks, where…