Related papers: How to Compute Times of Random Walks based Distrib…
Kemeny's constant for random walks on a graph is defined as the mean hitting time from one node to another selected randomly according to the stationary distribution. It has found numerous applications and attracted considerable research…
We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two…
In the last two decades we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs…
We analyze a class of distributed quantized consen- sus algorithms for arbitrary 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, and…
A recent result of Ding, Lee and Peres expresses the cover time of the random walk on a graph in terms of generic chaining for the commute distance. Their proof is very involved and the purpose of this article is to present a simpler…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
Analyzing social graphs with limited data access is challenging for third-party researchers. To address this challenge, a number of algorithms that estimate structural properties via a random walk have been developed. However, most existing…
We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…
This paper considers non-backtracking random walks on random graphs generated according to the configuration model. The quantity of interest is the scaling of the mixing time of the random walk as the number of vertices of the random graph…
Let $G$ be a directed graph with $n$ vertices and $m$ edges, embedded on a surface $S$, possibly with boundary, with first Betti number $\beta$. We consider the complexity of finding closed directed walks in $G$ that are either contractible…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
In this paper we propose algorithms for allocating $n$ sequential balls into $n$ bins that are interconnected as a $d$-regular $n$-vertex graph $G$, where $d\ge3$ can be any integer.Let $l$ be a given positive integer. In each round $t$,…
The rotor router model is a popular deterministic analogue of a random walk on a graph. Instead of moving to a random neighbor, the neighbors are served in a fixed order. We examine how fast this "deterministic random walk" covers all…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
We consider a decentralized learning setting in which data is distributed over nodes in a graph. The goal is to learn a global model on the distributed data without involving any central entity that needs to be trusted. While gossip-based…
Currently there are three major paradigms of quantum computation, the gate model, annealing, and walks on graphs. The gate model and quantum walks on graphs are universal computation models, while annealing plays within a specific subset of…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random…
We consider random walks on random graphs, focusing on return probabilities and hitting times for sparse Erdos-Renyi graphs. Using the tree approach which is expected to be exact in the large graph limit, we show how to solve for the…