Related papers: Multiple Random Walks on Graphs: Mixing Few to Cov…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
Various graph algorithms have been developed with multiple random walks, the movement of several independent random walkers on a graph. Designing an efficient graph algorithm based on multiple random walks requires investigating multiple…
We initiate the study of property testing in arbitrary planar graphs. We prove that bipartiteness can be tested in constant time, improving on the previous bound of $\tilde{O}(\sqrt{n})$ for graphs on $n$ vertices. The constant-time…
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 are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…
Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a…
We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this…
Random walks on expander graphs were thoroughly studied, with the important motivation that, under some natural conditions, these walks mix quickly and provide an efficient method of sampling the vertices of a graph. Alon, Benjamini,…
We introduce a new technique for bounding the cover time of random walks by relating it to the runtime of randomized broadcast. In particular, we strongly confirm for dense graphs the intuition of Chandra et al. \cite{CRRST97} that "the…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
The problem of sampling from the stationary distribution of a Markov chain finds widespread applications in a variety of fields. The time required for a Markov chain to converge to its stationary distribution is known as the classical…
Coalescing-branching random walks, or {\em cobra walks} for short, are a natural variant of random walks on graphs that can model the spread of disease through contacts or the spread of information in networks. In a $k$-cobra walk, at each…
We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a…
We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…