Fast Byzantine Gathering with Visibility in Graphs
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We consider the gathering task by a team of m synchronous mobile robots in a graph of n nodes. Each robot has an identifier (ID) and runs its own deterministic algorithm, i.e., there is no centralized coordinator. We consider a particularly challenging scenario: there are f Byzantine robots in the team that can behave arbitrarily, and even have the ability to change their IDs to any value at any time. There is no way to distinguish these robots from non-faulty robots, other than perhaps observing strange or unexpected behaviour. The goal of the gathering task is to eventually have all non-faulty robots located at the same node in the same round. It is known that no algorithm can solve this task unless there at least \(f+1\) non-faulty robots in the team. In this paper, we design an algorithm that runs in polynomial time with respect to n and m that matches this bound, i.e., it works in a team that has exactly \(f+1\) non-faulty robots. In our model, we have equipped the robots with sensors that enable each robot to see the subgraph (including robots) within some distance H of its current node. We prove that the gathering task is solvable if this visibility range H is at least the radius of the graph, and not solvable if H is any fixed constant.
KeywordsRobot gathering Byzantine faults Visibility Graphs Distributed algorithms
The authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), Discovery Grant RGPIN–2017–05936.
- 1.Barrameda, E.M., Santoro, N., Shi, W., Taleb, N.: Sensor deployment by a robot in an unknown orthogonal region: achieving full coverage. In: 20th IEEE International Conference on Parallel and Distributed Systems, ICPADS 2014, pp. 951–960 (2014). https://doi.org/10.1109/PADSW.2014.7097915
- 3.Bhagat, S., Mukhopadhyaya, K., Mukhopadhyaya, S.: Computation under restricted visibility. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, Current Research in Moving and Computing, vol. 11340, pp. 134–183. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_7CrossRefzbMATHGoogle Scholar
- 5.Bouchard, S., Dieudonné, Y., Lamani, A.: Byzantine gathering in polynomial time. In: 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018, pp. 147:1–147:15 (2018). https://doi.org/10.4230/LIPIcs.ICALP.2018.147
- 8.Cicerone, S., Stefano, G.D., 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, vol. 11340, pp. 184–217. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-D7_8CrossRefzbMATHGoogle Scholar
- 9.Défago, X., Potop-Butucaru, M., Tixeuil, S.: Fault-tolerant mobile robots. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, Current Research in Moving and Computing, vol. 11340, pp. 234–251. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_10CrossRefGoogle Scholar
- 11.Fischer, M., Jung, D., Meyer auf der Heide, F.: Gathering anonymous, oblivious robots on a grid. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 168–181. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_13CrossRefGoogle Scholar
- 14.Hirose, J., Nakamura, J., Ooshita, F., Inoue, M.: Gathering with a strong team in weakly byzantine environments. CoRR abs/2007.08217 (2020). https://arxiv.org/abs/2007.08217
- 15.Hsiang, T.-R., Arkin, E.M., Bender, M.A., Fekete, S.P., Mitchell, J.S.B.: Algorithms for rapidly dispersing robot swarms in unknown environments. In: Boissonnat, J.-D., Burdick, J., Goldberg, K., Hutchinson, S. (eds.) Algorithmic Foundations of Robotics V. STAR, vol. 7, pp. 77–93. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-45058-0_6CrossRefGoogle Scholar
- 18.Pelc, A.: Deterministic rendezvous algorithms. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities, Current Research in Moving and Computing, vol. 11340, pp. 423–454. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_17