Optimal patrolling of fragmented boundaries

Andrew Collins, Jurek Czyzowicz, Leszek Ga̧sieniec, Adrian Kosowski, Evangelos Kranakis, Danny Krizanc, Russell Martin, Oscar Morales Ponce

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Scopus citations

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 languageEnglish (US)
Title of host publicationSPAA 2013 - Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages241-250
Number of pages10
ISBN (Print)9781450315722
DOIs
StatePublished - 2013
Externally publishedYes
Event25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013 - Montreal, QC, Canada
Duration: Jul 23 2013Jul 25 2013

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013
CountryCanada
CityMontreal, QC
Period7/23/137/25/13

Keywords

  • Algorithms
  • Boundary patrolling
  • Idleness
  • Mobile robots

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

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  • Cite this

    Collins, A., Czyzowicz, J., Ga̧sieniec, L., Kosowski, A., Kranakis, E., Krizanc, D., Martin, R., & Ponce, O. M. (2013). Optimal patrolling of fragmented boundaries. In 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