Related papers: Deterministic Random Walks on the Two-Dimensional …
Rotor walks are cellular automata that determine deterministic traversals of particles in a directed multigraph using simple local rules, yet they can generate complex behaviors. Furthermore, these trajectories exhibit statistical…
Building on earlier work of Diaconis and Fulton (1991) and Lawler, Bramson, and Griffeath (1992), Propp in 2001 defined a deterministic analogue of internal diffusion-limited aggregation. This growth model is a "convergent game" of the sort…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
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…
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.…
We study exploration properties of a random walk on a network. For a fully connected network we find that the problem can be mapped to the well known coupon collector problem, thus allowing us to estimate form of $P(S,t)$: the distribution…
We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the…
The random walk is a fundamental stochastic process that underlies many numerical tasks in scientific computing applications. We consider here two neural algorithms that can be used to efficiently implement random walks on spiking…
Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong…
The simple random walk on $\mathbb{Z}^p$ shows two drastically different behaviours depending on the value of $p$: it is recurrent when $p\in\{1,2\}$ while it escapes (with a rate increasing with $p$) as soon as $p\geq3$. This classical…
We study rotor walk, a deterministic counterpart of the simple random walk, on infinite transient graphs. We show that the final rotor configuration of the rotor walk follows the law of the wired uniform spanning forest oriented toward…
Opportunistic routing is a multi-hop routing scheme which allows for selection of the best immediately available relay. In blind opportunistic routing protocols, where transmitters blindly broadcast without knowledge of the surrounding…
In [5], Holroyd, Levine, M\'esz\'aros, Peres, Propp and Wilson characterize recurrent chip-and-rotor configurations for strongly connected digraphs. However, the number of steps needed to recur, and the number of orbits is left open for…
Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion.…
In this paper, we propose a distributed algorithm to uniformly scatter the robots along a grid, with robots on alternate nodes of this grid distribution. These homogeneous, autonomous mobile robots place themselves equidistant apart on the…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
Deterministic walks over a random set of points in one and two dimensions (d=1,2) are considered. Points (``cities'') are randomly scattered in R^d following a uniform distribution. A walker (a ``tourist''), at each time step, goes to the…
Rotor-routing is a procedure for routing tokens through a network that can implement certain kinds of computation. These computations are inherently asynchronous (the order in which tokens are routed makes no difference) and distributed…