The traveling salesman problem with distances one and two
Mathematics of Operations Research
Approximation algorithms
Coverage for robotics – A survey of recent results
Annals of Mathematics and Artificial Intelligence
Competitive on-line coverage of grid environments by a mobile robot
Computational Geometry: Theory and Applications
Theoretical Analysis of the Multi-agent Patrolling Problem
IAT '04 Proceedings of the IEEE/WIC/ACM International Conference on Intelligent Agent Technology
Graph Theory
Fifty Years of Vehicle Routing
Transportation Science
Capacitated vehicle routing with non-uniform speeds
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Persistent ocean monitoring with underwater gliders: Adapting sampling resolution
Journal of Field Robotics
A Minimalist Algorithm for Multirobot Continuous Coverage
IEEE Transactions on Robotics
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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(logn)-approximation algorithm and an O(log脧聛G)-approximation algorithm, where 脧聛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.