Abstract
Exploration of different network topologies is one of the fundamental problems of distributed systems. The problem has been studied on networks like lines, rings, tori, rectangular grids, etc. In this work, we have considered a rectangle enclosed triangular grid (RETG). A RETG is a part of an infinite triangular grid and the part is enclosed by a rectangle whose one pair of parallel sides aligns with a family of parallel straight lines of the infinite triangular grid. We have studied the problem of perpetual exploration on a RETG using oblivious robots. We have considered the robots with limited visibility i.e. the robots are myopic. Infinite visibility becomes impractical for a very large network. Limited visibility is more practical than infinite visibility. The robots have neither any chirality nor any axis agreement. An algorithm is provided to explore the RETG perpetually without any collision. The algorithm works under a synchronous scheduler. The algorithm requires three robots with two hop visibility.
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References
Bramas, Q., Lafourcade, P., Devismes, S.: Optimal exclusive perpetual grid exploration by luminous myopic opaque robots with common chirality. Theor. Comput. Sci. 977, 114162 (2023). https://doi.org/10.1016/J.TCS.2023.114162
Rauch, A., Bramas, Q., Devismes, S., Lafourcade, P., Lamani, A.: Optimal exclusive perpetual grid exploration by luminous myopic robots without common chirality. In: Echihabi, K., Meyer, R. (eds.) Networked Systems—9th International Conference, NETYS 2021, Virtual Event, May 19-21, 2021, Proceedings. Lecture Notes in Computer Science, vol. 12754, pp. 95–110. Springer (2021). https://doi.org/10.1007/978-3-030-91014-3_7
Acknowledgement
The first author is supported by Council of Scientific & Industrial Research (CSIR), Govt. of India. The second author is supported by University Grants Commission (UGC), Govt. of India. The third author is supported by Science and Engineering Research Board (SERB), Govt. of India.
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Das, R., Goswami, P., Sau, B. (2025). Brief Announcement: Perpetual Exploration of Triangular Grid by Myopic Oblivious Robots Without Chirality. In: Masuzawa, T., Katayama, Y., Kakugawa, H., Nakamura, J., Kim, Y. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2024. Lecture Notes in Computer Science, vol 14931. Springer, Cham. https://doi.org/10.1007/978-3-031-74498-3_11
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DOI: https://doi.org/10.1007/978-3-031-74498-3_11
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