Related papers: Asymptotics for Push on the Complete Graph
We introduce a process where a connected rooted multigraph evolves by splitting events on its vertices, occurring randomly in continuous time. When a vertex splits, its incoming edges are randomly assigned between its offspring and a…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…
We prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…
We propose an algorithm for average consensus over a directed graph which is both fully asynchronous and robust to unreliable communications. We show its convergence to the average, while allowing for slowly growing but potentially…
A widely studied model of influence diffusion in social networks represents the network as a graph $G=(V,E)$ with an influence threshold $t(v)$ for each node. Initially the members of an initial set $S\subseteq V$ are influenced. During…
Quantum graphs with leads to infinity serve as convenient models for studying various aspects of systems which are usually attributed to chaotic scattering. They are also studied in several experimental systems and practical applications.…
Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to…
We develop an analytical model of information dissemination for a gossiping protocol that combines both pull and push approaches. With this model we analyse how fast an item is replicated through a network, and how fast the item spreads in…
We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…
In the on-line nearest-neighbour graph (ONG), each point after the first in a sequence of points in R^d is joined by an edge to its nearest-neighbour amongst those points that precede it in the sequence. We study the large-sample asymptotic…
In this work we address the question of efficiency of distributed computing in anonymous, congested and highly dynamic and not-always-connected networks/systems. More precisely, the system consists of an unknown number of anonymous nodes…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
The paper investigates efficient distributed computation in dynamic networks in which the network topology changes (arbitrarily) from round to round. Our first contribution is a rigorous framework for design and analysis of distributed…
We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph…
Gossip algorithms spread information by having nodes repeatedly forward information to a few random contacts. By their very nature, gossip algorithms tend to be distributed and fault tolerant. If done right, they can also be fast and…
We consider distributed plurality consensus in a complete graph of size $n$ with $k$ initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the…
We present a study of information flow that takes into account the observation that an item relevant to one person is more likely to be of interest to individuals in the same social circle than those outside of it. This is due to the fact…
We focus on the well-studied problem of distributed overlay network construction. We consider a synchronous gossip-based communication model where in each round a node can send a message of small size to another node whose identifier it…
In the voter model, each node of a graph has an opinion, and in every round each node chooses independently a random neighbour and adopts its opinion. We are interested in the consensus time, which is the first point in time where all nodes…