Related papers: A Cover Time Study of a non-Markovian Algorithm
Random walks are a fundamental primitive used in many machine learning algorithms with several applications in clustering and semi-supervised learning. Despite their relevance, the first efficient parallel algorithm to compute random walks…
We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that $n_1$, $n_2$, $n_3$, . . . distinct sites are visited at times $t_1$, $t_2$, $t_3$,…
Recently, in ["The coin-turning walk and its scaling limit", Electronic Journal of Probability, 25 (2020)], the ``coin-turning walk'' was introduced on ${\mathbb Z}$. It is a non-Markovian process where the steps form a (possibly)…
Random walks can be used to search a complex networks for a desired resource. To reduce the number of hops necessary to find the resource, we propose a search mechanism based on building random walks connecting together partial walks that…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
Learning to walk over a graph towards a target node for a given query and a source node is an important problem in applications such as knowledge base completion (KBC). It can be formulated as a reinforcement learning (RL) problem with a…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large graphs. We derive an exact formula valid for arbitrary graphs and arbitrary walks with stationary transition…
We present the first linear time complexity randomized algorithms for unbiased approximation of the celebrated family of general random walk kernels (RWKs) for sparse graphs. This includes both labelled and unlabelled instances. The…
This thesis explores a central question: how does memory affect the way random walkers explore space? By analyzing various non-Markovian models, where past behavior directly influences future dynamics, we uncover new mechanisms and…
Tree graphs are routinely used in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to…
We introduce a strategy of navigation in undirected networks, including regular, random, and complex networks, that is inspired by L\'evy random walks, generalizing previous navigation rules. We obtained exact expressions for the stationary…
We consider a modified random walk which uses unvisited edges whenever possible, and makes a simple random walk otherwise. We call such a walk an edge-process. We assume there is a rule A, which tells the walk which unvisited edge to use…
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. More precisely, for every D and C, there exists a=a(D,C)>0 such that for any graph G, with n vertices and…
We investigate multitarget search on complex networks and derive an exact expression for the mean random cover time that quantifies the expected time a walker needs to visit multiple targets. Based on this, we recover and extend some…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
The pivot algorithm is a Markov Chain Monte Carlo algorithm for simulating the self-avoiding walk. At each iteration a pivot which produces a global change in the walk is proposed. If the resulting walk is self-avoiding, the new walk is…
Graph sampling via crawling has been actively considered as a generic and important tool for collecting uniform node samples so as to consistently estimate and uncover various characteristics of complex networks. The so-called simple random…