Abstract
In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic bidirectional rings. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all k agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer \(g\,(< k)\), that agents terminate in a configuration such that either at least g agents or no agent exists at each node. The requirement for the partial gathering problem is strictly weaker than that for the total gathering problem, and thus it is interesting to clarify the difference in the move complexity between them. So far, partial gathering has been considered in static graphs. In this paper, we consider this problem in 1-interval connected rings, that is, one of the links in the ring may be missing at each time step. In such networks, we aim to clarify the solvability of the partial gathering problem and the move complexity, focusing on the relationship between values of k and g. First, we consider the case of \( 3g\le k\le 8g-2\). In this case, we show that our algorithm can solve the problem with the total number of O(kn) moves, where n is the number of nodes. Since \(k = O(g)\) holds when \(3g \le k \le 8g-2\), the move complexity O(kn) in this case can be represented also as O(gn). Next, we consider the case of \(k\ge 8g - 3\). In this case, we show that our algorithm can also solve the problem and its move complexity is O(gn). These results mean that, when \(k\ge 3g\), the partial gathering problem can be solved also in dynamic rings. In addition, agents require a total number of \(\varOmega (gn)\) (resp., \(\varOmega (kn)\)) moves to solve the partial (resp., total) gathering problem. Thus, the both proposed algorithms can solve the partial gathering problem with the asymptotically optimal total number of O(gn) moves, which is strictly smaller than that for the total gathering problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The knowledge of k is used for agents to decide which proposed algorithm they apply by comparing it with the value of g.
References
Baba, D., Izumi, T., Ooshita, F., Kakugawa, H., Masuzawa, T.: Linear time and space gathering of anonymous mobile agents in asynchronous trees. Theoret. Comput. Sci. 478, 118–126 (2013)
Das, S., Luna, D.G., Mazzei, D., Prencipe, G.: Compacting oblivious agents on dynamic rings. PeerJ Comput. Sci. 7, 1–29 (2021)
Dieudonné, Y., Pelc, A.: Anonymous meeting in networks. Algorithmica 74(2), 908–946 (2016). https://doi.org/10.1007/s00453-015-9982-0
Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple mobile agent rendezvous in a ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24698-5_62
Gotoh, T., Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T.: Group exploration of dynamic tori. In: ICDCS, pp. 775–785 (2018)
Gray, R.S., Kotz, D., Cybenko, G., Rus, D.: D’agents: applications and performance of a mobile-agent system. Softw. Pract. Exper. 32(6), 543–573 (2002)
Kranakis, E., Krizanc, D., Markou, E.: Mobile agent rendezvous in a synchronous torus. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 653–664. Springer, Heidelberg (2006). https://doi.org/10.1007/11682462_60
Kranakis, E., Krozanc, D., Markou, E.: The mobile agent rendezvous problem in the ring. Syn. Lect. Distrib. Comput. Theory 1, 1–122 (2010)
Kranakis, E., Santoro, N., Sawchuk, C., Krizanc, D.: Mobile agent rendezvous in a ring. In: ICDCS, pp. 592–599 (2003)
Lange, D., Oshima, M.: Seven good reasons for mobile agents. CACM 42(3), 88–89 (1999)
Di Luna, G., Dobrev, S., Flocchini, P., Santoro, N.: Distributed exploration of dynamic rings. Distrib. Comput. 33(1), 41–67 (2018). https://doi.org/10.1007/s00446-018-0339-1
Luna, D.G., Flocchini, P., Pagli, L., Prencipe, G., Santoro, N., Viglietta, G.: Gathering in dynamic rings. Theoret. Comput. Sci. 811, 79–98 (2018)
Shibata, M., Kawai, S., Ooshita, F., Kakugawa, H., Masuzawa, T.: Partial gathering of mobile agents in asynchronous unidirectional rings. Theoret. Comput. Sci. 617, 1–11 (2016)
Shibata, M., Kawata, N., Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T.: Move-optimal partial gathering of mobile agents without identifiers or global knowledge in asynchronous unidirectional rings. Theoret. Comput. Sci. 822, 92–109 (2020)
Shibata, M., Nakamura, D., Ooshita, F., Kakugawa, H., Masuzawa, T.: Partial gathering of mobile agents in arbitrary networks. IEICE Trans. Inf. Syst. 102(3), 444–453 (2019)
Shibata, M., Ooshita, F., Kakugawa, H., Masuzawa, T.: Move-optimal partial gathering of mobile agents in asynchronous trees. Theoret. Comput. Sci. 705, 9–30 (2018)
Shibata, M., Sudo, Y., Nakamura, J., Kim, Y.: Uniform deployment of mobile agents in dynamic rings. In: Devismes, S., Mittal, N. (eds.) SSS 2020. LNCS, vol. 12514, pp. 248–263. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64348-5_20
Shibata, M., Tixeuil, S.: Partial gathering of mobile robots from multiplicity-allowed configurations in rings. In: Devismes, S., Mittal, N. (eds.) SSS 2020. LNCS, vol. 12514, pp. 264–279. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64348-5_21
Acknowledgement
This work was partially supported by JSPS KAKENHI Grant Number 18K18029, 18K18031, 20H04140, 20KK0232, and 21K17706; the Hibi Science Foundation; and Foundation of Public Interest of Tatematsu.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Shibata, M., Sudo, Y., Nakamura, J., Kim, Y. (2021). Partial Gathering of Mobile Agents in Dynamic Rings. In: Johnen, C., Schiller, E.M., Schmid, S. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2021. Lecture Notes in Computer Science(), vol 13046. Springer, Cham. https://doi.org/10.1007/978-3-030-91081-5_29
Download citation
DOI: https://doi.org/10.1007/978-3-030-91081-5_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-91080-8
Online ISBN: 978-3-030-91081-5
eBook Packages: Computer ScienceComputer Science (R0)