Abstract
In this paper, we consider the partial gathering problem of mobile agents in asynchronous unidirectional rings. This problem requires that, for a given positive integer g, all the agents terminate in a configuration such that at least g agents or no agent exist at each node. While the previous work achieves move-optimal partial gathering using distinct IDs or knowledge of the number of agents, in this paper we aim to achieve this without such information. We consider deterministic and randomized cases. First, in the deterministic case, we show that unsolvable initial configurations exist. In addition, we propose an algorithm to solve the problem from any solvable initial configuration in O(gn) total number of moves, where n is the number of nodes. Next, in the randomized case, we propose an algorithm to solve the problem in O(gn) expected total number of moves from any initial configuration. Since agents require \(\varOmega (gn)\) total number of moves to solve the partial gathering problem, our algorithms can solve the problem in asymptotically optimal total number of moves without global knowledge.
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Notes
- 1.
Even if \(a_i\) becomes inactive, it does not happen that all the active agents become inactive because we consider the case of \(\textit{peri}\ge g\).
- 2.
We consider the situation for explanation, and it is possible that some agents execute the second part and the other agents still execute the first part.
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Acknowledgement
This work was partially supported by JSPS KAKENHI Grant Number 17K19977, 18K18000, 18K11167, 18K18031, and 19K11826, and Japan Science and Technology Agency (JST) SICORP.
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Shibata, M., Kawata, N., Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T. (2019). Partial Gathering of Mobile Agents Without Identifiers or Global Knowledge in Asynchronous Unidirectional Rings. In: Censor-Hillel, K., Flammini, M. (eds) Structural Information and Communication Complexity. SIROCCO 2019. Lecture Notes in Computer Science(), vol 11639. Springer, Cham. https://doi.org/10.1007/978-3-030-24922-9_19
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