Related papers: Using First Hitting Times to Find Sets that Maximi…
Theoretical computer science plays an important role in the understanding of social networks and their properties. We can model information rippling throughout social networks, or the opinions of social media users for example, using graph…
Motivated by applications in telecommunications, computer scienceand physics, we consider a discrete-time Markov process withrestart. At each step the process eitherwith a positive probability restarts from a given distribution, orwith the…
We consider a consensus algorithm in which every node in a sequence of undirected, B-connected graphs assigns equal weight to each of its neighbors. Under the assumption that the degree of each node is fixed (except for times when the node…
We consider the weight design problem for the consensus algorithm under a finite time horizon. We assume that the underlying network is random where the links fail at each iteration with certain probability and the link failures can be…
The control and risk assessment in complex information systems require to take into account extremes arising from nodes with large node degrees. Various sampling techniques like a Page Rank random walk, a Metropolis-Hastings Markov chain…
We study the popular distributed consensus method over networks composed of a number of densely connected clusters with a sparse connection between them. In these cluster networks, the method often constitutes two-time-scale dynamics, where…
We investigate exceedances of the process over a sufficiently high threshold. The exceedances determine the risk of hazardous events like climate catastrophes, huge insurance claims, the loss and delay in telecommunication networks. Due to…
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…
In this paper we introduce the notion of optimization under control and communication constraint in a robotic network. Starting from a general setup, we focus our attention on the problem of achieving rendezvous in minimum time for a…
We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…
This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model…
Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…
We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the…
In this letter, we study the problem of accelerating reaching average consensus over connected graphs in a discrete-time communication setting. Literature has shown that consensus algorithms can be accelerated by increasing the graph…
Previous researches have shown that adding local memory can accelerate the consensus. It is natural to ask questions like what is the fastest rate achievable by the $M$-tap memory acceleration, and what are the corresponding control…
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,…
The first passage time (FPT) for random walks is a key indicator of how fast information diffuses in a given system. Despite the role of FPT as a fundamental feature in transport phenomena, its behavior, particularly in heterogeneous…
This paper considers the consensus problem for a network of nodes with random interactions and sampled-data control actions. We first show that consensus in expectation, in mean square, and almost surely are equivalent for a general random…
In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic…
We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of…