Abstract
The gathering problem of anonymous and oblivious mobile robots is one of fundamental problems in the theoretical mobile robotics. We consider the gathering problem in unoriented and anonymous rings, which requires that all robots gather at a non-predefined node. Since the gathering problem cannot be solved without any additional capability to robots, all the previous works assume some capability of robots, such as accessing the memory on node. In this paper, we focus on the multiplicity capability. This paper presents a deterministic gathering algorithm with local-weak multiplicity, which provides the robot with the information about whether its current node has more than one robot or not. This assumption is strictly weaker than that by previous works. Moreover, we show that our algorithm is asymptotically time-optimal one, that is, the time complexity of our algorithm is O(n), where n is the number of nodes. Interestingly, in spite of assuming the weaker assumption, it achieves significant improvement compared to the previous algorithm, which takes O(kn) time for k robots.
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Izumi, T., Izumi, T., Kamei, S., Ooshita, F. (2010). Mobile Robots Gathering Algorithm with Local Weak Multiplicity in Rings. In: Patt-Shamir, B., Ekim, T. (eds) Structural Information and Communication Complexity. SIROCCO 2010. Lecture Notes in Computer Science, vol 6058. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13284-1_9
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DOI: https://doi.org/10.1007/978-3-642-13284-1_9
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