Related papers: Cover times of random searches
The speed of an exhaustive search can be measured by a cover time, which is defined as the time it takes a random searcher to visit every state in some target set. Cover times have been studied in both the physics and probability…
We present an analytical method for computing the mean cover time of a random walk process on arbitrary, complex networks. The cover time is defined as the time a random walker requires to visit every node in the network at least once. This…
The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short range memory. We derive the exact…
Cover times measure the speed of exhaustive searches which require the exploration of an entire spatial region(s). Applications include the immune system hunting pathogens, animals collecting food, robotic demining or cleaning, and computer…
Given a traversal algorithm, cover time is the expected number of steps needed to visit all nodes in a given graph. A smaller cover time means a higher exploration efficiency of traversal algorithm. Although random walk algorithms have been…
We consider a minimal model of persistent random searcher with short range memory. We calculate exactly for such searcher the mean first-passage time to a target in a bounded domain and find that it admits a non trivial minimum as function…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
Cover times quantify the speed of exhaustive search. In this work, we compute exactly the mean cover time associated with a one-dimensional Brownian search under exponentially distributed resetting. We also approximate the moments of cover…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
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 pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
The territory explored by a random walk is a key property that may be quantified by the number of distinct sites that the random walk visits up to a given time. The extent of this spatial exploration characterizes many important physical,…
Among observables characterising the random exploration of a graph or lattice, the cover time, namely the time to visit every site, continues to attract widespread interest. Much insight about cover times is gained by mapping to the…
We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c \ge 3$). Starting from a random initial node at time $t=1$, at each time step $t \ge…
The cover-time problem, i.e., time to visit every site in a system, is one of the key issues of random walks with wide applications in natural, social, and engineered systems. Addressing the full distribution of cover times for random walk…
Search patterns of randomly oriented steps of different lengths have been observed on all scales of the biological world, ranging from the microscopic to the ecological, including in protein motors, bacteria, T-cells, honeybees, marine…
We introduce a formalism based on a continuous time approximation, to study the characteristics of Page Rank random walks. We find that the diffusion of the occupancy probability has a dynamics that exponentially "forgets" the initial…
We consider information diffusion on Web-like networks and how random walks can simulate it. A well-studied problem in this domain is Partial Cover Time, i.e., the calculation of the expected number of steps a random walker needs to visit a…