Related papers: Walking Randomly, Massively, and Efficiently

We study the random walk problem on a class of deterministic Scale-Free networks displaying a degree sequence for hubs scaling as a power law with an exponent $\gamma=\log 3/\log2$. We find exact results concerning different first-passage…

In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…

For a generalized step reinforced random walk, starting from the origin, the first step is taken according to the first element of an innovation sequence. Then in subsequent epochs, it recalls a past epoch with probability proportional to a…

A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…

Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…

In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian…

We propose a computationally efficient random walk on a convex body which rapidly mixes and closely tracks a time-varying log-concave distribution. We develop general theoretical guarantees on the required number of steps; this number can…

Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…

We investigate whether there are inherent limits of parallelization in the (randomized) massively parallel computation (MPC) model by comparing it with the (sequential) RAM model. As our main result, we show the existence of hard functions…

In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…

Given a set of graphs from some unknown family, we want to generate new graphs from that family. Recent methods use diffusion on either graph embeddings or the discrete space of nodes and edges. However, simple changes to embeddings (say,…

The node2vec random walk is a non-Markovian random walk on the vertex set of a graph, widely used for network embedding and exploration. This random walk model is defined in terms of three parameters which control the probability of,…

We consider an optimal flow distribution problem in which the goal is to find a radial configuration that minimizes resistance-induced quadratic distribution costs while ensuring delivery of inputs from multiple sources to all sinks to meet…

We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…

Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…

Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…

Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We…