Complete Visibility Algorithm for Autonomous Mobile Luminous Robots under an Asynchronous Scheduler on Grid Plane (2306.08354v1)
Abstract: An autonomous mobile robot system is a distributed system consisting of mobile computational entities (called robots) that autonomously and repeatedly perform three operations: Look, Compute, and Move. Various problems related to autonomous mobile robots, such as gathering, pattern formation, or flocking, have been extensively studied to understand the relationship between each robot's capabilities and the solvability of these problems. In this study, we focus on the complete visibility problem, which involves relocating all the robots on an infinite grid plane such that each robot is visible to every other robot. We assume that each robot is a luminous robot (i.e., has a light with a constant number of colors) and opaque (not transparent). In this paper, we propose an algorithm to achieve complete visibility when a set of robots is given. The algorithm ensures that complete visibility is achieved even when robots operate asynchronously and have no knowledge of the total number of robots on the grid plane using only two colors.
- Gathering autonomous mobile robots. In Proc. of the 9th International Colloquium on Structural Information and Communication Complexity, volume 13 of Proceedings in Informatics, pages 57–72. Carleton Scientific, 2002.
- Uniform scattering of autonomous mobile robots in a grid. In 23rd IEEE International Symposium on Parallel and Distributed Processing, IPDPS, pages 1–8, 2009.
- Hard tasks for weak robots: The role of common knowledge in pattern formation by autonomous mobile robots. In Algorithms and Computation, 10th Int. Symposium, ISAAC, volume 1741 of Lecture Notes in Computer Science, pages 93–102, 1999. doi:10.1007/3-540-46632-0_10. URL https://doi.org/10.1007/3-540-46632-0_10.
- Mutual visibility by luminous robots without collisions. Inf. Comput., 254:392–418, 2017.
- Mutual visibility with an optimal number of colors. In 11th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS, volume 9536 of LNCS, pages 196–210, 2015a.
- Robots with lights: Overcoming obstructed visibility without colliding. In Stabilization, Safety, and Security of Distributed Systems SSS, volume 8756 of LNCS, pages 150–164, 2014a.
- The mutual visibility problem for oblivious robots. In Proc. of the 26th Canadian Conference on Computational Geometry, CCCG, 2014b.
- Bounds on mutual visibility algorithms. In Proceedings of the 27th Canadian Conference on Computational Geometry, CCCG, 2015b.
- Optimal randomized complete visibility on a grid for asynchronous robots with lights. In 2020 IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW, pages 607–616, 2020.
- Optimal randomized complete visibility on a grid for asynchronous robots with lights. Int. J. Netw. Comput., 11(1):50–77, 2021.
- Complete visibility for robots with lights in O(1) time. In Stabilization, Safety, and Security of Distributed Systems SSS, volume 10083 of LNCS, pages 327–345, 2016.
- O(log n)-time complete visibility for asynchronous robots with lights. In 2017 IEEE International Parallel and Distributed Processing Symposium, IPDPS, pages 513–522, 2017.
- Mutual visibility by asynchronous robots on infinite grid. In 14th International Symposium on Algorithms and Experiments for Wireless Sensor Networks, ALGOSENSORS, volume 11410 of LNCS, pages 83–101, 2018.
- Achim Flammenkamp. Progress in the no-three-in-line-problem. J. Comb. Theory, Ser. A, 60(2):305–311, 1992.
- K. F. Roth. On a problem of heilbronn. Journal of The London Mathematical Society-second Series, pages 198–204, 1951.
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