### Abstract

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].

Original language | English (US) |
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Title of host publication | SPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures |

Publisher | Association for Computing Machinery |

Pages | 241-250 |

Number of pages | 10 |

ISBN (Print) | 9781450315722 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

Event | 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013 - Montreal, QC, Canada Duration: Jul 23 2013 → Jul 25 2013 |

### Publication series

Name | Annual ACM Symposium on Parallelism in Algorithms and Architectures |
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### Conference

Conference | 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013 |
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Country | Canada |

City | Montreal, QC |

Period | 7/23/13 → 7/25/13 |

### Keywords

- Algorithms
- Boundary patrolling
- Idleness
- Mobile robots

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture

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## Cite this

*SPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures*(pp. 241-250). (Annual ACM Symposium on Parallelism in Algorithms and Architectures). Association for Computing Machinery. https://doi.org/10.1145/2486159.2486176