相关论文: Deterministic Random Walks on the Integers
Consider the following computational problem: given a regular digraph $G=(V,E)$, two vertices $u,v \in V$, and a walk length $t\in \mathbb{N}$, estimate the probability that a random walk of length $t$ from $u$ ends at $v$ to within $\pm…
The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of…
We analyze a deterministic form of the random walk on the integer line called the {\em liar machine}, similar to the rotor-router model, finding asymptotically tight pointwise and interval discrepancy bounds versus random walk. This…
We study a discrete time self interacting random process on graphs, which we call Greedy Random Walk. The walker is located initially at some vertex. As time evolves, each vertex maintains the set of adjacent edges touching it that have not…
Random walks on dynamic graphs have received increasingly more attention from different academic communities over the last decade. Despite the relatively large literature, little is known about random walks that construct the graph where…
Rotor walk is a deterministic analogue of simple random walk. For any given graph, we construct a rotor configuration for which the escape rate of the corresponding rotor walk is equal to the escape rate of simple random walk, and thus…
Given a random walk $(S_n)$ with typical step distributed according to some fixed law and a fixed parameter $p \in (0,1)$, the associated positively step-reinforced random walk is a discrete-time process which performs at each step, with…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…
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 study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
Performing random walks in networks is a fundamental primitive that has found applications in many areas of computer science, including distributed computing. In this paper, we focus on the problem of sampling random walks efficiently in a…
We introduce a non-equilibrium discrete-time random walk model on multiplex networks, in which at each time step the walker first undergoes a random jump between neighboring nodes in the same layer, and then tries to hop from one node to…
We study a family of correlated one-dimensional random walks with a finite memory range M.These walks are extensions of the Taylor's walk as investigated by Goldstein, which has a memory range equal to one. At each step, with a probability…
We revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and…
Random walks on graphs can be slow. To speed them up, imagine that at each step instead of choosing the neighbor at random, there is a small probability $\varepsilon>0$ that we can choose it. We show that in this case, at least for graphs…
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…
A step-reinforced random walk is a discrete-time non-Markovian process with long range memory. At each step, with a fixed probability p, the positively step-reinforced random walk repeats one of its preceding steps chosen uniformly at…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
We construct the conditional version of $k$ independent and identically distributed random walks on $\R$ given that they stay in strict order at all times. This is a generalisation of so-called non-colliding or non-intersecting random…
This paper considers a class of non-Markovian discrete-time random processes on a finite state space {1,...,d}. The transition probabilities at each time are influenced by the number of times each state has been visited and by a fixed a…