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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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)
Bajaj, C.: The algebraic degree of geometric optimization problems. Discrete Comput. Geom. 3, 177–191 (1988)
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)
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)
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_9
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)
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41(4), 829–879 (2012)
Cieliebak, M., Prencipe, G.: Gathering autonomous mobile robots. In: 9th International Colloquium on Structural Information and Communication Complexity (SIROCCO), pp. 57–72 (2002)
Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34, 1516–1528 (2005)
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_45
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_52
Czyzowicz, J., Gasieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. Theor. Comput. Sci. 410, 481–499 (2009)
Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: Autonomous mobile robots with lights. Theor. Comput. Sci. 609, 171–184 (2016)
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_4
Défago, X., Gradinariu, M., Messika, S., Raipin Parvédy, P.: Fault and byzantine tolerant self-stabilizing mobile robots gathering - feasibility study. Technical report (2016)
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)
Durocher, S., Kirkpatrick, D.: The projection median of a set of points. Comput. Geom.: Theory Appl. 42(5), 364–375 (2009)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous mobile robots with limited visibility. Theor. Comput. Sci. 337, 147–168 (2005)
Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Rendezvous with constant memory. Theor. Comput. Sci. 621, 57–72 (2016)
Fu**aga, N., Yamauchi, Y., Kijima, S., Yamashita, M.: Asynchronous pattern formation by anonymous oblivious mobile robots. SIAM J. Comput. 44(3), 740–785 (2015)
Gan Chaudhuri, S., Mukhopadhyaya, K.: Leader election and gathering for asynchronous fat robots without common chirality. J. Discrete Algorithms 33, 171–192 (2015)
Heriban, A., Défago, X., Tixeuil, S.: Optimally gathering two robots. In: 19th International Conference on Distributed Computing and Networking (ICDCN), pp. 1–10 (2018)
Izumi, T., et al.: The gathering problem for two oblivious robots with unreliable compasses. SIAM J. Comput. 41(1), 26–46 (2012)
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_12
Kupitz, Y., Martini, H.: Geometric aspects of the generalized Fermat-Torricelli problem. Intuitive Geom. 6, 55–127 (1997)
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)
Pagli, L., Prencipe, G., Viglietta, G.: Getting close without touching: near-gathering for autonomous mobile robots. Distrib. Comput. 28(5), 333–349 (2015)
Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384(2–3), 222–231 (2007)
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)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)
Weiszfeld, E.: Sur le point pour lequel la somme des distances de \(n\) points donnés est minimum. Tohoku Math. 43, 355–386 (1936)
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Flocchini, P. (2019). Gathering. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-11072-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-11071-0
Online ISBN: 978-3-030-11072-7
eBook Packages: Computer ScienceComputer Science (R0)