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Evacuating an Equilateral Triangle in the Face-to-Face Model

Authors Huda Chuangpishit, Saeed Mehrabi, Lata Narayanan, Jaroslav Opatrny

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Huda Chuangpishit
Saeed Mehrabi
Lata Narayanan
Jaroslav Opatrny

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Huda Chuangpishit, Saeed Mehrabi, Lata Narayanan, and Jaroslav Opatrny. Evacuating an Equilateral Triangle in the Face-to-Face Model. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 11:1-11:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.OPODIS.2017.11

Abstract

Consider k robots initially located at the centroid of an equilateral triangle T of sides of length one. The goal of the robots is to evacuate T through an exit at an unknown location on the boundary of T. Each robot can move anywhere in T independently of other robots with maximum speed one. The objective is to minimize the evacuation time, which is defined as the time required for all k robots to reach the exit. We consider the face-to-face communication model for the robots: a robot can communicate with another robot only when they meet in T. In this paper, we give upper and lower bounds for the face-to-face evacuation time by k robots. We show that for any k, any algorithm for evacuating k >= 1 robots from T requires at least sqrt(3) time. This bound is asymptotically optimal, as we show that a straightforward strategy of evacuation by k robots gives an upper bound of sqrt(3) + 3/k. For k = 3, 4, 5, 6, we show significant improvements on the obvious upper bound by giving algorithms with evacuation times of 2.0887, 1.9816, 1.876, and 1.827, respectively. For k = 2 robots, we give a lower bound of 1 + 2/sqrt(3) ~= 2.154, and an algorithm with upper bound of 2.3367 on the evacuation time.
Keywords
  • Distributed algorithms
  • Robots evacuation
  • Face-to-face communication
  • Equilateral triangle

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References

  1. R. Ahlswede and I. Wegener. Search problems. Wiley-Interscience, 1987. Google Scholar
  2. R. A. Baeza-Yates, J. C. Culberson, and G. J. E. Rawlins. Searching with uncertainty (extended abstract). In Proceedings of the 1st Scandinavian Workshop on Algorithm Theory (SWAT 88), pages 176-189, 1988. Google Scholar
  3. R. A. Baeza-Yates and R. Schott. Parallel searching in the plane. Computational Geometry, 5:143-154, 1995. Google Scholar
  4. A. Beck. On the linear search problem. Israel Journal of Mathematics, 2(4):221-228, 1964. Google Scholar
  5. A. Bonato and R. Nowakowski. The Game of Cops and Robbers on Graphs. American Mathematical Society, 2011. Google Scholar
  6. S. Brandt, K.-T. Forster, B. Richner, and R. Wattenhofer. Wireless evacuation on m rays with k searchers. In Proceedings of SIROCCO 2017, to appear, 2017. Google Scholar
  7. M. Chrobak, L. Gasieniec, T. Gorry, and R. Martin. Group search on the line. In Proceedings of SOFSEM 2015: 41st International Conference on Current Trends in Theory and Practice of Computer Science, pages 164-176, 2015. Google Scholar
  8. J. Czyzowicz, L. Gasieniec, T. Gorry, E. Kranakis, R. Martin, and D. Pajak. Evacuating robots via unknown exit in a disk. In Proceedings of the 28th International Symposium on Distributed Computing (DISC 2014), Austin, TX, USA, pages 122-136, 2014. Google Scholar
  9. J. Czyzowicz, K. Georgiou, M. Godon, E. Kranakis, D. Krizanc, W. Rytter, and M. Wlodarczyk. Evacuation from a disc in the presence of a faulty robot. In Proceedings of SIROCCO 2017, to appear, 2017. Google Scholar
  10. J. Czyzowicz, K. Georgiou, E. Kranakis, L. Narayanan, J. Opatrny, and B. Vogtenhuber. Evacuating robots from a disk using face-to-face communication (extended abstract). In Proceedings of the 9th International Conference on Algorithms and Complexity (CIAC 2015), Paris, France, pages 140-152, 2015. Google Scholar
  11. J. Czyzowicz, E. Kranakis, D. Krizanc, L. Narayanan, J. Opatrny, and S. M. Shende. Wireless autonomous robot evacuation from equilateral triangles and squares. In Proceedings of the 14th International Conference on Ad-hoc, Mobile, and Wireless Networks (ADHOC-NOW 2015), Athens, Greece, pages 181-194, 2015. Google Scholar
  12. Y. Emek, T. Langner, J. Uitto, and R. Wattenhofer. Solving the ANTS problem with asynchronous finite state machines. In Proceedings of the 41st International Colloquium on Automata, Languages, and Programming, (ICALP 2014), Part II, pages 471-482, 2014. Google Scholar
  13. O. Feinerman and A. Korman. Theoretical distributed computing meets biology: A review. In Proceedings of the 9th International Conference on Distributed Computing and Internet Technology, (ICDCIT 2013), Bhubaneswar, India, pages 1-18, 2013. Google Scholar
  14. O. Feinerman, A. Korman, Z. Lotker, and J.-S. Sereni. Collaborative search on the plane without communication. In ACM Symposium on Principles of Distributed Computing (PODC 2012), Funchal, Madeira, Portugal, pages 77-86, 2012. Google Scholar
  15. P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci., 337(1-3):147-168, 2005. Google Scholar
  16. S. K. Ghosh and R. Klein. Online algorithms for searching and exploration in the plane. Computer Science Review, 4(4):189-201, 2010. Google Scholar
  17. L. Hua and E. K. P. Chong. Search on lines and graphs. In Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, China, pages 5780-5785, 2009. Google Scholar
  18. A. Jez and J. Lopuszanski. On the two-dimensional cow search problem. Information Processing Letters, 109(11):543-547, 2009. Google Scholar
  19. C. Lenzen, N. A. Lynch, C. C. Newport, and T. Radeva. Trade-offs between selection complexity and performance when searching the plane without communication. In ACM Symposium on Principles of Distributed Comp. (PODC 2014),, pages 252-261, 2014. Google Scholar
  20. A. López-Ortiz and G. Sweet. Parallel searching on a lattice. In Proceedings of the 13th Canadian Conference on Computational Geometry (CCCG 2001), pages 125-128, 2001. Google Scholar
  21. P. Nahin. Chases and Escapes: The Mathematics of Pursuit and Evasion. Princeton University Press, 2012. Google Scholar
  22. L. D. Stone. Theory of Optimal Search. Academic Press New York, 1975. Google Scholar
  23. I. Thompson. Understanding Maple. Cambridge University Press, 2016. Google Scholar
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