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Computational geometry column 59

Published: 09 June 2014 Publication History

Abstract

This column is about patrolling problems in a geometric network. Mobile agents patrol a road network, and have to visit every point in the network as frequently as possible. The goal is finding a schedule that minimizes the idle time, i.e., the maximum time between two consecutive visits of some agent over all points in the network.

References

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N. Agmon, S. Kraus, and G. A. Kaminka, Multi-robot perimeter patrol in adversarial settings, in Proc. International Conference on Robotics and Automation (ICRA 2008), IEEE, 2008, pp. 2339--2345.
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T. Bohman, R. Holzman, and D. Kleitman, Six lonely runners, Electronic Journal of Combinatorics 8 (2001), R3.
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Y. Chevaleyre, Theoretical analysis of the multi-agent patrolling problem, in Proc. International Conference on Intelligent Agent Technology (IAT 2004), IEEE, 2004, pp. 302--308.
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H. Choset, Coverage for robotics|a survey of recent results, Annals of Mathematics and Artificial Intelligence 31 (2001), 113--126.
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A. Collins, J. Czyzowicz, L. Gasieniec, A. Kosowski, E. Kranakis, D. Krizanc, R. Martin and O. M. Ponce, Optimal patrolling of fragmented boundaries, in Proc. 25th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2013), ACM, 2013, pp. 241--250.
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T. W. Cusick, View-obstruction problems, Aequationes Math. 9 (1973), 165--170.
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T. W. Cusick and C. Pomerance, View-obstruction problems III, Journal of Number Theory 19 (1984), 131--139.
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J. Czyzowicz, L. Gasieniec, A. Kosowski, and E. Kranakis, Boundary patrolling by mobile agents with distinct maximal speeds, in Proc. 19th European Symposium on Algorithms (ESA 2011), LNCS 6942, Springer, 2011, pp. 701--712.
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A. Dumitrescu, A. Ghosh, and Cs. D. Tóth, On fence patrolling by mobile agents, preprint, January 2014; arXiv:1401.6070.
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Y. Elmaliach, N. Agmon, and G. A. Kaminka, Multi-robot area patrol under frequency constraints, in Proc. International Conference on Robotics and Automation (ICRA 2007), IEEE, 2007, pp. 385--390.
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A. Kawamura and Y. Kobayashi, Fence patrolling by mobile agents with distinct speeds, in Proc. 23rd International Symposium on Algorithms and Computation (ISAAC 2012), LNCS 7676, Springer, 2012, pp. 598--608.
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A. Machado, G. Ramalho, J. D. Zucker, and A. Drogoul, Multi-agent patrolling: an empirical analysis of alternative architectures, 3rd International Workshop on Multi-Agent-Based Simulation, Springer, 2002, pp. 155--170.
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J. M. Wills, Zwei Sátze über inhomogene diophantische Approximation von Irrationalzahlen, Monatshefte für Mathematik 71(3) (1967), 263--269.

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Published In

cover image ACM SIGACT News
ACM SIGACT News  Volume 45, Issue 2
June 2014
100 pages
ISSN:0163-5700
DOI:10.1145/2636805
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 June 2014
Published in SIGACT Volume 45, Issue 2

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Author Tags

  1. approximation algorithm
  2. fence patrolling
  3. idle time
  4. mobile agents
  5. runners

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  • (2020)Simple strategies versus optimal schedules in multi-agent patrollingTheoretical Computer Science10.1016/j.tcs.2020.07.037Online publication date: Aug-2020
  • (2020)Problems on track runnersComputational Geometry10.1016/j.comgeo.2020.101611(101611)Online publication date: Feb-2020
  • (2019)Approximation Algorithms for Barrier Sweep CoverageInternational Journal of Foundations of Computer Science10.1142/S012905411950013830:03(425-448)Online publication date: 30-Apr-2019
  • (2015)Approximation algorithm for sweep coverage on graphInformation Processing Letters10.1016/j.ipl.2015.03.011115:9(712-718)Online publication date: 1-Sep-2015
  • (2015)Simple Strategies Versus Optimal Schedules in Multi-agent PatrollingProceedings of the 9th International Conference on Algorithms and Complexity - Volume 907910.1007/978-3-319-18173-8_19(261-273)Online publication date: 20-May-2015

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