Abstract
We present the problem of finding a maximal independent set (MIS) (named as MIS Filling problem) of an arbitrary connected graph with luminous myopic mobile robots. The robots enter the graph one after another from a particular vertex called the Door and move along the edges of the graph without collision to occupy vertices such that the set of occupied vertices forms a maximal independent set.
This paper explores two versions of the MIS filling problem. For the MIS Filling with Single Door case, our IND algorithm forms an MIS of size m in \(O(m^2)\) epochs under an asynchronous scheduler, where an epoch is the smallest time interval in which each participating robot gets activated and executes the algorithm at least once. The robots have three hops of visibility range, \(\varDelta + 8\) number of colors, and \(O(\log \varDelta )\) bits of persistent storage, where \(\varDelta \) is the maximum degree of the graph. For the MIS Filling with Multiple Doors case, our MULTIND algorithm forms an MIS in \(O(m^2)\) epochs under a semi-synchronous scheduler using robots with five hops of visibility range, \(\varDelta + k + 7\) number of colors, and \(O(\log (\varDelta + k))\) bits of persistent storage, where k is the number of doors.
P.S.Mandal—Partially supported by SERB, Govt. of India, Grant Number: MTR/2019/001528
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Pramanick, S., Samala, S.V., Pattanayak, D., Mandal, P.S. (2023). Filling MIS Vertices of a Graph by Myopic Luminous Robots. In: Molla, A.R., Sharma, G., Kumar, P., Rawat, S. (eds) Distributed Computing and Intelligent Technology. ICDCIT 2023. Lecture Notes in Computer Science, vol 13776. Springer, Cham. https://doi.org/10.1007/978-3-031-24848-1_1
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