Related papers: The Nearest Unvisited Vertex Walk on Random Graphs
Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…
In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent…
Consider a system of $K$ particles moving on the vertex set of a finite connected graph with at most one particle per vertex. If there is one, the particle at $x$ chooses one of the $\hbox{deg} (x)$ neighbors of its location uniformly at…
A random walk on a $N$-dimensional hypercube is a discrete time stochastic process whose state space is the set $\{-1,+1\}^{N}$, which has uniform probability of reaching any neighbour state, and probability zero of reaching a non-neighbour…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…
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…
In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last \tau steps. This procedure leads to trajectories composed of a transient part…
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…
The random walk with choice is a well known variation to the random walk that first selects a subset of $d$ neighbours nodes and then decides to move to the node which maximizes the value of a certain metric; this metric captures the number…
We present a deterministic algorithm that given a tree T with n vertices, a starting vertex v and a slackness parameter epsilon > 0, estimates within an additive error of epsilon the cover and return time, namely, the expected time it takes…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping independent and identically distributed coins. A deterministic…
We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop an…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
Consider a symmetric aperiodic random walk in $Z^d$, $d\geq 3$. There are points (called heavy points) where the number of visits by the random walk is close to its maximum. We investigate the local times around these heavy points and show…
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…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time on any n-vertex, connected graph is at least (1+o(1)) n…
We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…