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Gathering

  • Paola Flocchini
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11340)

Abstract

In this Chapter, we focus on the Gathering problem: that is, the problem of having the robots, initially located in arbitrary distinct points of the plane, gather in the exact same location. In this Chapter we examine Gathering in the standard \(\mathcal{OBLOT}\) model when robots have unlimited visibility; we also briefly review results about the relaxed problem of Convergence, where robots only need to move infinitely close to each other, without necessarily reaching the same point.

References

  1. 1.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: A distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robot. Autom. 15(5), 818–828 (1999)CrossRefGoogle Scholar
  2. 2.
    Bajaj, C.: The algebraic degree of geometric optimization problems. Discrete Comput. Geom. 3, 177–191 (1988)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bhagat, S., Gan Chaudhuri, S., Mukhopadhyaya, K.: Fault-tolerant gathering of asynchronous oblivious mobile robots under one-axis agreement. J. Discrete Algorithms 36, 50–62 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bhagat, S., Gan Chaudhuri, S., Mukhopadhyaya, K.: Gathering of opaque robots in 3D space. In: 19th International Conference on Distributed Computing and Networking (ICDCN), pp. 1–10 (2018)Google Scholar
  5. 5.
    De Carufel, J.-L., Flocchini, P.: Fault-induced dynamics of oblivious robots on a line. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 126–141. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-69084-1_9CrossRefGoogle Scholar
  6. 6.
    Cicerone, S., Di Stefano, G., Navarra, A.: Gathering of robots on meeting-points: feasibility and optimal resolution algorithms. Distrib. Comput. 31(1), 1–50 (2018)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Cieliebak, M., Prencipe, G.: Gathering autonomous mobile robots. In: 9th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp. 57–72 (2002)Google Scholar
  9. 9.
    Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34, 1516–1528 (2005)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors and movements. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 549–560. Springer, Heidelberg (2006).  https://doi.org/10.1007/11672142_45CrossRefGoogle Scholar
  11. 11.
    Cord-Landwehr, A., et al.: A new approach for analyzing convergence algorithms for mobile robots. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 650–661. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22012-8_52CrossRefGoogle Scholar
  12. 12.
    Czyzowicz, J., Gasieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. Theor. Comput. Sci. 410, 481–499 (2009)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: Autonomous mobile robots with lights. Theor. Comput. Sci. 609, 171–184 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Défago, X., Gradinariu, M., Messika, S., Raipin-Parvédy, P.: Fault-tolerant and self-stabilizing mobile robots gathering. In: Dolev, S. (ed.) DISC 2006. LNCS, vol. 4167, pp. 46–60. Springer, Heidelberg (2006).  https://doi.org/10.1007/11864219_4CrossRefGoogle Scholar
  15. 15.
    Défago, X., Gradinariu, M., Messika, S., Raipin Parvédy, P.: Fault and byzantine tolerant self-stabilizing mobile robots gathering - feasibility study. Technical report (2016)Google Scholar
  16. 16.
    Di Luna, G., Flocchini, P., Santoro, N., Viglietta, G.: Turingmobile: a turing machine of oblivious mobile robots with limited visibility and its applications. In: 32nd International Symposium on Distributed Computing (DISC) (2018)Google Scholar
  17. 17.
    Durocher, S., Kirkpatrick, D.: The projection median of a set of points. Comput. Geom.: Theory Appl. 42(5), 364–375 (2009)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous mobile robots with limited visibility. Theor. Comput. Sci. 337, 147–168 (2005)CrossRefGoogle Scholar
  19. 19.
    Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Rendezvous with constant memory. Theor. Comput. Sci. 621, 57–72 (2016)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fujinaga, N., Yamauchi, Y., Kijima, S., Yamashita, M.: Asynchronous pattern formation by anonymous oblivious mobile robots. SIAM J. Comput. 44(3), 740–785 (2015)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gan Chaudhuri, S., Mukhopadhyaya, K.: Leader election and gathering for asynchronous fat robots without common chirality. J. Discrete Algorithms 33, 171–192 (2015)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Heriban, A., Défago, X., Tixeuil, S.: Optimally gathering two robots. In: 19th International Conference on Distributed Computing and Networking (ICDCN), pp. 1–10 (2018)Google Scholar
  23. 23.
    Izumi, T., et al.: The gathering problem for two oblivious robots with unreliable compasses. SIAM J. Comput. 41(1), 26–46 (2012)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Katreniak, B.: Convergence with limited visibility by asynchronous mobile robots. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 125–137. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22212-2_12CrossRefGoogle Scholar
  25. 25.
    Kupitz, Y., Martini, H.: Geometric aspects of the generalized Fermat-Torricelli problem. Intuitive Geom. 6, 55–127 (1997)MathSciNetzbMATHGoogle Scholar
  26. 26.
    Lin, J., Morse, A.S., Anderson, B.D.O.: The multi-agent rendezvous problem. Part 2: the asynchronous case. SIAM J. Control. Optim. 46(6), 2120–2147 (2007)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Pagli, L., Prencipe, G., Viglietta, G.: Getting close without touching: near-gathering for autonomous mobile robots. Distrib. Comput. 28(5), 333–349 (2015)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384(2–3), 222–231 (2007)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Souissi, S., Défago, X., Yamashita, M.: Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. ACM Trans. Auton. Adapt. Syst. 4(1), 1–27 (2009)CrossRefGoogle Scholar
  30. 30.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Weiszfeld, E.: Sur le point pour lequel la somme des distances de \(n\) points donnés est minimum. Tohoku Math. 43, 355–386 (1936)zbMATHGoogle Scholar
  32. 32.
    Yamamoto, K., Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: The optimal tolerance of uniform observation error for mobile robot convergence. Theor. Comput. Sci. 444, 77–86 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.University of OttawaOttawaCanada

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