Art gallery theorems and algorithms
Art gallery theorems and algorithms
Information Processing Letters
Shortest watchman routes in simple polygons
Discrete & Computational Geometry
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Watchman routes under limited visibility
Computational Geometry: Theory and Applications
Information Sciences: an International Journal
Touring a sequence of polygons
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Information Processing Letters
Theoretical Analysis of the Multi-agent Patrolling Problem
IAT '04 Proceedings of the IEEE/WIC/ACM International Conference on Intelligent Agent Technology
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
A realistic model of frequency-based multi-robot polyline patrolling
Proceedings of the 7th international joint conference on Autonomous agents and multiagent systems - Volume 1
On redundancy, efficiency, and robustness in coverage for multiple robots
Robotics and Autonomous Systems
Behavioral control for multi-robot perimeter patrol: a finite state automata approach
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Multi-agent patrolling: an empirical analysis of alternative architectures
MABS'02 Proceedings of the 3rd international conference on Multi-agent-based simulation II
Computing multiple watchman routes
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Multi-robot area patrol under frequency constraints
Annals of Mathematics and Artificial Intelligence
Autonomous multi-agent cycle based patrolling
ANTS'10 Proceedings of the 7th international conference on Swarm intelligence
Boundary patrolling by mobile agents with distinct maximal speeds
ESA'11 Proceedings of the 19th European conference on Algorithms
Algorithmica
Watchman tours for polygons with holes
Computational Geometry: Theory and Applications
Approximation algorithms for art gallery problems in polygons and terrains
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
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A set of mobile robots is deployed on a simple curve of finite length, composed of a finite set of vital segments separated by neutral segments. The robots have to patrol the vital segments by perpetually moving on the curve, without exceeding their uniform maximum speeds. The quality of patrolling is measured by the idleness, i.e., the longest time period during which any vital point on the curve is not visited by any robot. Given a configuration of vital segments, our goal is to provide algorithms describing the movement of the robots along the curve so as to minimize the idleness. Our main contribution is a proof that the optimal solution to the patrolling problem is attained either by the cyclic strategy, in which all the robots move in one direction around the curve, or by the partition strategy, in which the curve is partitioned into sections which are patrolled separately by individual robots. These two fundamental types of strategies were studied in the past in the robotics community in different theoretical and experimental settings. However, to our knowledge, this is the first theoretical analysis proving optimality in such a general scenario. Throughout the paper we assume that all robots have the same maximum speed. In fact, the claim is known to be invalid when this assumption does not hold, cf. [Czyzowicz et al., Proc. ESA 2011].