English
Related papers

Related papers: Estimating Random-Walk Probabilities in Directed G…

200 papers

We consider the quantity $P(G)$ associated with a graph $G$ that is defined as the probability that a randomly chosen subtree of $G$ is spanning. Motivated by conjectures due to Chin, Gordon, MacPhee and Vincent on the behaviour of this…

Combinatorics · Mathematics 2019-10-17 Stephan Wagner

We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…

Machine Learning · Statistics 2024-05-27 Isaac Reid , Eli Berger , Krzysztof Choromanski , Adrian Weller

We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…

Data Structures and Algorithms · Computer Science 2018-05-01 Saeed Akhoondian Amiri , Klaus-Tycho Foerster , Stefan Schmid

Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…

Probability · Mathematics 2018-10-09 Ruojun Huang

We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show…

Distributed, Parallel, and Cluster Computing · Computer Science 2011-10-18 Danupon Nanongkai , Atish Das Sarma , Gopal Pandurangan

Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was…

Networking and Internet Architecture · Computer Science 2009-04-17 Konstantin Avrachenkov , Vivek Borkar , Danil Nemirovsky

For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems (MBPs) with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front,…

Numerical Analysis · Mathematics 2023-12-04 Surendra Nepal , Magnus Ogren , Yosief Wondmagegne , Adrian Muntean

In a former paper we simplified the proof of a theorem on personalized random walk that is fundamental to graph nodes clustering and generalized it to bipartite graphs for a specific case where the proobability of random jump was…

Social and Information Networks · Computer Science 2017-02-14 Mieczysław A. Kłopotek , Sławomir T. Wierzchom , Robert A. Kłopotek , Elżbieta A. Kłopotek

This paper proposes a Galton board approximation method to analyze the potential walking preferences of pedestrians. We employ the binomial distribution to estimate the walking preferences of pedestrians in dynamic crowds. Estimating the…

Physics and Society · Physics 2024-10-18 Jinghui Wang , Wei Lv

This work considers the low-rank approximation of a matrix $A(t)$ depending on a parameter $t$ in a compact set $D \subset \mathbb{R}^d$. Application areas that give rise to such problems include computational statistics and dynamical…

Numerical Analysis · Mathematics 2024-04-18 Daniel Kressner , Hei Yin Lam

We present the analytical and numerical results of a random walk on the family of small-world graphs. The average access time shows a crossover from the regular to random behavior with increasing distance from the starting point of the…

Statistical Mechanics · Physics 2009-10-31 Sagar A. Pandit , R. E. Amritkar

We give a deterministic, nearly logarithmic-space algorithm that given an undirected graph $G$, a positive integer $r$, and a set $S$ of vertices, approximates the conductance of $S$ in the $r$-step random walk on $G$ to within a factor of…

Computational Complexity · Computer Science 2019-11-26 Jack Murtagh , Omer Reingold , Aaron Sidford , Salil Vadhan

Recommender systems typically suggest to users content similar to what they consumed in the past. If a user happens to be exposed to strongly polarized content, she might subsequently receive recommendations which may steer her towards more…

Computers and Society · Computer Science 2023-04-27 Francesco Fabbri , Yanhao Wang , Francesco Bonchi , Carlos Castillo , Michael Mathioudakis

Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…

Combinatorics · Mathematics 2022-06-14 Stefan Steinerberger , Rekha R. Thomas

Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph P_{n}, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set…

Combinatorics · Mathematics 2013-07-23 Chris Dowden

Previous work has shown the effectiveness of random walk hitting times as a measure of dissimilarity in a variety of graph-based learning problems such as collaborative filtering, query suggestion or finding paraphrases. However,…

Data Structures and Algorithms · Computer Science 2013-04-17 Joel Lang , James Henderson

In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…

Data Structures and Algorithms · Computer Science 2016-11-03 Michael B. Cohen , Jon Kelner , John Peebles , Richard Peng , Aaron Sidford , Adrian Vladu

Probabilistic recurrence relations (PRRs) are a standard formalism for describing the runtime of a randomized algorithm. Given a PRR and a time limit $\kappa$, we consider the classical concept of tail probability $\Pr[T \ge \kappa]$, i.e.,…

Data Structures and Algorithms · Computer Science 2023-05-25 Yican Sun , Hongfei Fu , Krishnendu Chatterjee , Amir Kafshdar Goharshady

We study the problem of searching for a fixed path $\epsilon_0\epsilon_1\cdots\epsilon_l$ on a network through random walks. We analyze the first hitting time of tracking the path, and obtain exact expression of mean first hitting time…

Disordered Systems and Neural Networks · Physics 2010-07-13 Shao-Ping Wang , Wen-Jiang Pei

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…

Combinatorics · Mathematics 2017-02-15 Dmitri Fomin