Abstract
This paper addresses one of the fundamental geometric formation problems, namely the mutual visibility problem, for a set of semi-synchronous, opaque robots occupying distinct positions in the Euclidean plane. Since robots are opaque, if three robots lie on a line, the middle robot obstructs the visions of the two other robots. The mutual visibility problem requires the robots to coordinate their movements to form a configuration, within finite time and without collision, in which no three robots are collinear. We assume that robots are endowed with constant bits of persistent memory. We consider the 
computational model [4] in which the persistent memory is used by the robots only to remember their previous internal states. This piece of information is not communicated or visible to the other robots. Except from this persistent memory, robots are oblivious i.e., they do not carry forward any other information from their previous computational cycles. The paper presents a distributed algorithm to solve the mutual visibility problem for a set of semi-synchronous robots using only 1 bit of persistent memory. The proposed algorithm also provides a self-stabilizing solution to the problem. The algorithm does not impose any other restriction on the capability of the robots and guarantees collision-free movements for the robots.
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References
Das, S., Flocchini, P., Prencipe, G., Santoro, N., Yamashita, M.: The power of lights: synchronizing asynchronous robots using visible bits. In: Proceedings of 32nd International Conference on Distributed Computing Systems (ICDCS), pp. 506–515 (2012)
Bhagat, S., Chaudhuri, S.G., Mukhopadhyaya, K.: Formation of general position by asynchronous mobile robots under one-axis agreement. In: Kaykobad, M., Petreschi, R. (eds.) WALCOM 2016. LNCS, vol. 9627, pp. 80–91. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-30139-6_7
Flocchini, P., Prencipe, G., Santoro, N.: Distributed Computing by Oblivious Mobile Robots. Morgan & Claypool, San Rafael (2012)
Flocchini, P., Santoro, N., Viglietta, G., Yamashita, M.: Rendezvous of two robots with constant memory. In: Moscibroda, T., Rescigno, A.A. (eds.) SIROCCO 2013. LNCS, vol. 8179, pp. 189–200. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03578-9_16
Aljohani, A., Sharma, G.: Complete visibility for mobile robots with lights tolerating faults. Int. J. Netw. Comput. 8(1), 32–52 (2018)
Aljohani, A., Poudel, P., Sharma, G.: Fault-tolerant complete visibility for asynchronous robots with lights under one-axis agreement. In: Rahman, M.S., Sung, W.-K., Uehara, R. (eds.) WALCOM 2018. LNCS, vol. 10755, pp. 169–182. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75172-6_15
Sharma, G., Alsaedi, R., Busch, C., Mukhopadhyay, S.: The complete visibility problem for fat robots with lights. In: Proceedings of 19th International Conference on Distributed Computing and Networking (ICDCN 2018), p. 21 (2018)
Sharma, G., Vaidyanathan, R., Trahan, J.L.: Constant-time complete visibility for asynchronous robots with lights. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 265–281. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69084-1_18
Bhagat, S., Mukhopadhyaya, K.: Optimum algorithm for mutual visibility among asynchronous robots with lights. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 341–355. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69084-1_24
Sharma, G., Busch, C., Mukhopadhyay, S.: Mutual visibility with an optimal number of colors. In: Bose, P., Gąsieniec, L.A., Römer, K., Wattenhofer, R. (eds.) ALGOSENSORS 2015. LNCS, vol. 9536, pp. 196–210. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-28472-9_15
Sharma, G., Busch, C., Mukhopadhyay, S.: Bounds on mutual visibility algorithms. In: Proceedings of 27th Canadian Conference on Computational Geometry (CCCG 2015) (2015)
Di Luna, G.A., Flocchini, P., Gan Chaudhuri, S., Poloni, F., Santoro, N., Viglietta, G.: Mutual visibility by luminous robots without collisions. In: Information and Computation, vol. 254, pp. 392–418 (2017)
Di Luna, G.A., Flocchini, P., Poloni, F., Santoro, N., Viglietta, G.: The mutual visibility problem for oblivious robots. In: Proceedings of 26th Canadian Conference on Computational Geometry (CCCG 2014) (2014)
Sharma, G.: Mutual visibility for robots with lights tolerating light faults. In: Proceedings of IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), pp. 829–836 (2018)
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Bhagat, S., Mukhopadhyaya, K. (2019). Mutual Visibility by Robots with Persistent Memory. In: Chen, Y., Deng, X., Lu, M. (eds) Frontiers in Algorithmics. FAW 2019. Lecture Notes in Computer Science(), vol 11458. Springer, Cham. https://doi.org/10.1007/978-3-030-18126-0_13
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