离散环境中的持续监测：最小化观测之间的最大加权延迟
Persistent Monitoring in Discrete Environments: Minimizing the Maximum Weighted Latency Between Observations
摘要：
在本文中，我们考虑的问题规划的路径，机器人监测一组已知的功能感兴趣的环境中。我们将环境表示为具有顶点权重和边长度的图。顶点表示感兴趣的区域，边长度给出区域之间的旅行时间，顶点权重给出每个区域的重要性。当机器人在图上重复执行闭合行走时，我们将顶点的加权延迟定义为访问该顶点之间的最大时间，由该顶点的重要性（顶点权重）加权。我们的目标是找到一个封闭的行走，最大限度地减少任何顶点的最大加权延迟。我们表明，不存在一个多项式时间算法的问题。然后，我们提供了两个近似算法;一个$O(\log n)$近似算法和一个$O(\log ρ_G)$近似算法，其中$ρ_G$是最大和最小顶点权重之间的比率。我们提供的模拟结果表明，我们的算法可以应用到由数千个顶点组成的问题，和一个案例研究巡逻城市的犯罪。
英文摘要：
In this paper, we consider the problem of planning a path for a robot to monitor a known set of features of interest in an environment. We represent the environment as a graph with vertex weights and edge lengths. The vertices represent regions of interest, edge lengths give travel times between regions, and the vertex weights give the importance of each region. As the robot repeatedly performs a closed walk on the graph, we define the weighted latency of a vertex to be the maximum time between visits to that vertex, weighted by the importance (vertex weight) of that vertex. Our goal is to find a closed walk that minimizes the maximum weighted latency of any vertex. We show that there does not exist a polynomial time algorithm for the problem. We then provide two approximation algorithms; an $O(\log n)$-approximation algorithm and an $O(\log ρ_G)$-approximation algorithm, where $ρ_G$ is the ratio between the maximum and minimum vertex weights. We provide simulation results which demonstrate that our algorithms can be applied to problems consisting of thousands of vertices, and a case study for patrolling a city for crime.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
