Abstract
The Gathering task by means of a swarm of robots disposed on the vertices of a graph requires robots to move toward a common vertex from where they do not move anymore.
When dealing with very weak robots in terms of capabilities, considering synchronous or asynchronous settings may heavily affect the feasibility of the problem. In fact, even though dealing with asynchronous robots in general requires more sophisticated strategies with respect to the synchronous counterpart, sometimes it comes out that asynchronous robots simply cannot solve the problem whereas synchronous robots can. We study general properties of graphs that can be exploited in order to accomplish the gathering task in the synchronous setting, obtaining an interesting sufficient condition for the feasibility, applicable to any topology. We then consider dense and symmetric graphs like complete and complete bipartite graphs where asynchronous robots cannot solve much. In such topologies we fully characterize the solvability of the gathering task in the synchronous setting by suitably combining some strategies arising by the general approach with specific techniques dictated by the considered topologies.
The work has been supported in part by the European project “Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies” (GEO-SAFE), contract no. H2020-691161, and by the Italian National Group for Scientific Computation (GNCS-INdAM).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Babai, L., Kucera, L.: Canonical labelling of graphs in linear average time. In: 20th Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 29–31 October 1979, pp. 39–46. IEEE Computer Society (1979)
Babai, L., Luks, E.M.: Canonical labeling of graphs. In: Proceedings of the 15th Annual ACM Symposium on Theory of Computing, Boston, Massachusetts, USA, 25–27 April 1983, pp. 171–183. ACM (1983)
Bose, K., Kundu, M.K., Adhikary, R., Sau, B.: Optimal gathering by asynchronous oblivious robots in hypercubes. In: Gilbert, S., Hughes, D., Krishnamachari, B. (eds.) ALGOSENSORS 2018. LNCS, vol. 11410, pp. 102–117. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14094-6_7
Cicerone, S., Di Stefano, G., Navarra, A.: Minimum-traveled-distance gathering of oblivious robots over given meeting points. In: Gao, J., Efrat, A., Fekete, S.P., Zhang, Y. (eds.) ALGOSENSORS 2014. LNCS, vol. 8847, pp. 57–72. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46018-4_4
Cicerone, S., Di Stefano, G., Navarra, A.: MinMax-distance gathering on given meeting points. In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 127–139. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18173-8_9
Cicerone, S., Di Stefano, G., Navarra, A.: Asynchronous robots on graphs: gathering. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities: Current Research in Moving and Computing. LNCS, vol. 11340, pp. 184–217. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_8
Cicerone, S., Stefano, G.D., 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)
D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of robots on anonymous grids and trees without multiplicity detection. Theor. Comput. Sci. 610, 158–168 (2016)
D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering asynchronous and oblivious robots on basic graph topologies under the look-compute-move model. In: Alpern, S., Fokkink, R., Gąsieniec, L., Lindelauf, R., Subrahmanian, V. (eds.) Search Theory: A Game Theoretic Perspective, pp. 197–222. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-6825-7_13
D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering on rings under the look-compute-move model. Distrib. Comput. 27(4), 255–285 (2014)
D’Angelo, G., Di Stefano, G., Navarra, A., Nisse, N., Suchan, K.: Computing on rings by oblivious robots: a unified approach for different tasks. Algorithmica 72(4), 1055–1096 (2015)
D’Angelo, G., Navarra, A., Nisse, N.: A unified approach for gathering and exclusive searching on rings under weak assumptions. Distrib. Comput. 30(1), 17–48 (2017)
D’Angelo, G., Stefano, G.D., Navarra, A.: Gathering six oblivious robots on anonymous symmetric rings. J. Discrete Algorithms 26, 16–27 (2014)
D’Emidio, M., Di Stefano, G., Frigioni, D., Navarra, A.: Characterizing the computational power of mobile robots on graphs and implications for the Euclidean plane. Inf. Comput. 263, 57–74 (2018)
Di Stefano, G., Navarra, A.: Gathering of oblivious robots on infinite grids with minimum traveled distance. Inf. Comput. 254, 377–391 (2017)
Di Stefano, G., Navarra, A.: Optimal gathering of oblivious robots in anonymous graphs and its application on trees and rings. Distrib. Comput. 30(2), 75–86 (2017)
Guilbault, S., Pelc, A.: Gathering asynchronous oblivious agents with local vision in regular bipartite graphs. Theor. Comput. Sci. 509, 86–96 (2013)
Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Time-optimal gathering algorithm of mobile robots with local weak multiplicity detection in rings. IEICE Trans. 96–A(6), 1072–1080 (2013)
Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: gathering of many asynchronous oblivious robots on a ring. Theor. Comput. Sci. 411, 3235–3246 (2010)
Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008)
McKay, B.D.: Practical graph isomorphism. Congressus Numerantium 30, 45–87 (1981)
Miyazaki, T.: The complexity of McKay’s canonical labeling algorithm. In: Groups and Computation, Proceedings of a DIMACS Workshop, New Brunswick, New Jersey, USA, 7–10 June 1995, pp. 239–256 (1995)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Cicerone, S., Di Stefano, G., Navarra, A. (2019). Gathering Synchronous Robots in Graphs: From General Properties to Dense and Symmetric Topologies. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-24922-9_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-24921-2
Online ISBN: 978-3-030-24922-9
eBook Packages: Computer ScienceComputer Science (R0)