相关论文: Robotic Surveillance Based on the Meeting Time of …

This article rigorously analyzes the meeting time between pursuers and evaders performing random walks on digraphs. There exist several bounds on the expected meeting time between random walkers on graphs in the literature, however,…

In this paper, we revisit the problem of classical \textit{meeting times} of random walks in graphs. In the process that two tokens (called agents) perform random walks on an undirected graph, the meeting times are defined as the expected…

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 prove new results on lazy random walks on finite graphs. To start, we obtain new estimates on return probabilities $P^t(x,x)$ and the maximum expected hitting time $t_{\rm hit}$, both in terms of the relaxation time. We also prove a…

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…

Given a two-dimensional polygonal space, the multi-robot visibility-based pursuit-evasion problem tasks several pursuer robots with the goal of establishing visibility with an arbitrarily fast evader. The best known complete algorithm for…

We suggest a non-asymptotic matrix perturbation-theoretic approach to get sharp bounds on the expected meeting time of random walks on large (possibly random) graphs. We provide a formula for the expected meeting time in terms of the…

With the increasing use of robots in daily life, there is a growing need to provide robust collaboration protocols for robots to tackle more complicated and dynamic problems effectively. This paper presents a novel, factor graph-based…

The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for…

In this paper we consider a robot patrolling problem in which events arrive randomly over time at the vertices of a graph. When an event arrives it remains active for a random amount of time. If that time active exceeds a certain threshold,…

Consider a random walk on a tree $G=(V,E)$. For $v,w \in V$, let the hitting time $H(v,w)$ denote the expected number of steps required for the random walk started at $v$ to reach $w$, and let $\pi_v = \mathrm{deg}(v)/2|E|$ denote the…

We analyse the problem of meeting times for interdependent stochastic agents: random walkers whose behaviour is stochastic but controlled by their selections from some set of allowed actions, and the inference problem of when these agents…

The expected meeting time of two random walkers on an undirected graph of size $N$, where at each time step one walker moves and the process stops when they collide, satisfies a system of $\binom{N}{2}$ linear equations. Na\"{i}vely,…

We consider two random walks evolving synchronously on a random out-regular graph of $n$ vertices with bounded out-degree $r\ge 2$, also known as a random Deterministic Finite Automaton (DFA). We show that, with high probability with…

Given a mapped environment, we formulate the problem of visually tracking and following an evader using a probabilistic framework. In this work, we consider a non-holonomic robot with a limited visibility depth sensor in an indoor…

We consider a pursuit-evasion scenario involving a group of pursuers and a single evader in a two-dimensional unbounded environment. The pursuers aim to capture the evader in finite time while ensuring the evader remains enclosed within the…

This paper studies a multi-robot visibility-based pursuit-evasion problem in which a group of pursuer robots are tasked with detecting an evader within a two dimensional polygonal environment. The primary contribution is a novel formulation…

We investigate the hitting times of random walks on graphs, where a hitting time is defined as the number of steps required for a random walker to move from one node to another. While much of the existing literature focuses on calculating…

We present an analytical approach to study simple symmetric random walks (RWs) on a crossing geometry consisting of a plane square lattice crossed by $n_l$ number of lines that all meet each other at a single point (the origin) on the…

Researchers have designed many algorithms to measure the distances between graph nodes, such as average hitting times of random walks, cosine distances from DeepWalk, personalized PageRank, etc. Successful although these algorithms are,…