Abstract
In this paper, we consider the uniform deployment problem of mobile agents in asynchronous unidirectional ring networks. This problem requires agents to spread uniformly in the network. In this paper, we focus on the memory space per agent required to solve the problem. We consider two problem settings. The first setting assumes that agents have no multiplicity detection, that is, agents cannot detect whether another agent is staying at the same node or not. In this case, we show that each agent requires \(\varOmega (\log n)\) memory space to solve the problem, where n is the number of nodes. In addition, we propose an algorithm to solve the problem with \(O(k + \log n)\) memory space per agent, where k is the number of agents. The second setting assumes that each agent is equipped with the weak multiplicity detection, that is, agents can detect another agent staying at the same node, but cannot learn the exact number. Then, we show that the memory space per agent can be reduced to \(O(\log k + \log \log n)\). To the best of our knowledge, this is the first research considering the effect of the multiplicity detection on memory space required to solve problems.
A preliminary brief announcement of this work appeared in the proceedings of the 19th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2017). This work was partially supported by JSPS KAKENHI Grant Number 16K00018, 17K19977, and 18K18031, and Japan Science and Technology Agency (JST) SICORP.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
In practice, each node can store more information, but it is sufficient to store information about tokens when considering anonymous agents.
- 2.
This is why such multiplicity detection is called weak.
- 3.
We assume this for simplicity, but even if two or more agents exist at the same node in \(C_0\), agents can solve the problem similarly by using the number of tokens at each node and atomicity of execution.
- 4.
This definition is based on the ideal time complexity for asynchronous message-passing systems [9].
- 5.
Each agent can detect when it completes one circuit of the ring using knowledge of k.
- 6.
When an agent in the selection phase visits \(v_j\), it leaves \(v_j\) without staying there by the atomicity of an action. Hence, the behavior of leader agent \(a_i\) can inform a follower agent of the beginning of the collection phase.
- 7.
By the atomicity of an action, when an agent moves to some leader node, the leader agent already starts its collection phase and leaves the leader node.
References
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)
Lange, D.B., Oshima, M.: Seven good reasons for mobile agents. CACM 42(3), 88–89 (1999)
Kranakis, E., Krizanc, D.: An algorithmic theory of mobile agents. In: Montanari, U., Sannella, D., Bruni, R. (eds.) TGC 2006. LNCS, vol. 4661, pp. 86–97. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75336-0_6
Cao, J., Sun, Y., Wang, X., Das, S.K.: Scalable load balancing on distributed web servers using mobile agents. JPDC 63(10), 996–1005 (2003)
Flocchini, P., Prencipe, G., Santoro, N.: Self-deployment of mobile sensors on a ring. Theor. Comput. Sci. 402(1), 67–80 (2008)
Yotam, E., Alfred, B.M.: Uniform multi-agent deployment on a ring. Theor. Comput. Sci. 412(8), 783–795 (2011)
Barriere, L., Flocchini, P., Mesa-Barrameda, E., Santoro, N.: Uniform scattering of autonomous mobile robots in a grid. Int. J. Found. Comput. Sci. 22(03), 679–697 (2011)
Shibata, M., Mega, T., Ooshita, F., Kakugawa, H., Masuzawa, T.: Uniform deployment of mobile agents in asynchronous rings. In: PODC, pp. 415–424 (2016)
Tel, G.: Introduction to Distributed Algorithms. Cambridge University Press, Cambridge (2000)
Amos, O.R., Benjamin, P.: Residue Number Systems: Theory and Implementation, vol. 2. World Scientific, Singapore (2007)
Pei, D., Salomaa, A., Ding, C.: Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography. World Scientific, Singapore (1996)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Shibata, M., Kakugawa, H., Masuzawa, T. (2018). Space-Efficient Uniform Deployment of Mobile Agents in Asynchronous Unidirectional Rings. In: Lotker, Z., Patt-Shamir, B. (eds) Structural Information and Communication Complexity. SIROCCO 2018. Lecture Notes in Computer Science(), vol 11085. Springer, Cham. https://doi.org/10.1007/978-3-030-01325-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-01325-7_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-01324-0
Online ISBN: 978-3-030-01325-7
eBook Packages: Computer ScienceComputer Science (R0)