Realization of Periodic Functions by Self-stabilizing Population Protocols with Synchronous Handshakes

Lamani, Anissa; Yamashita, Masafumi

doi:10.1007/978-3-319-49001-4_2

Cited by 6 publications

(6 citation statements)

References 9 publications

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“…The uniform bipartition problem is a special case of a group composition problem, which divides a population into multiple groups to satisfy some conditions. Some protocols for the group composition problem are developed as subroutines to realize fault-tolerant protocols [20] and periodic functions [21]. However, the complexity of the problem has not been studied deeply yet.…”

Section: The Backgroundmentioning

confidence: 99%

“…As a similar problem to the uniform bipartition problem, a group composition problem is studied in [20], [21]. Delporte-Gallet et al [20] proposed a protocol to divide a population into g groups of almost the same size.…”

Section: Related Workmentioning

confidence: 99%

“…However, the paper does not consider other setting. Lamani et al [21] studied a problem that divides a population into groups of designated sizes. Although the proposed protocols assume arbitrary initial states, they also assume that n/2 pairs of agents make interactions at the same time and that agents know n. In addition, the protocol requires n states, that is, it is not a constant-space protocol.…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Space-Optimal Population Protocols for Uniform Bipartition Under Global Fairness

Yasumi

Ooshita

Yamaguchi

et al. 2019

IEICE Trans. Inf. & Syst.

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Hiroto YASUMI †a) , Student Member, Fukuhito OOSHITA †b) , Ken'ichi YAMAGUCHI † †c) , Members, and Michiko INOUE †d) , Senior Member SUMMARYIn this paper, we consider a uniform bipartition problem in a population protocol model. The goal of the uniform bipartition problem is to divide a population into two groups of the same size. We study the problem under global fairness with various assumptions: 1) a population with or without a base station, 2) symmetric or asymmetric protocols, and 3) designated or arbitrary initial states. As a result, we completely clarify solvability of the uniform bipartition problem under global fairness and, if solvable, show the tight upper and lower bounds on the number of states. key words: population protocol, uniform bipartition, distributed protocol

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Section: The Backgroundmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Space-Optimal Population Protocols for Uniform Bipartition Under Global Fairness

Yasumi

Ooshita

Yamaguchi

et al. 2019

IEICE Trans. Inf. & Syst.

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show abstract

“…As a similar problem to the uniform k-partition problem, Lamani et al [19] studied a group composition problem that divides a population into groups of designated sizes. Although the proposed protocols assume arbitrary initial states, they also assume that n/2 pairs of agents make interactions simultaneously and that all agents know n. Therefore the protocol does not work in our setting.…”

Section: Related Workmentioning

confidence: 99%

A Population Protocol for Uniform k-partition under Global Fairness

Yasumi

Kitamura

Ooshita

et al. 2019

IJNC

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In this paper, we consider a uniform k-partition problem in a population protocol model. The uniform k-partition problem divides a population into k groups of the same size. For this problem, we give a symmetric protocol with designated initial states under global fairness. The proposed protocol requires 3k − 2 states for each agent. Since any protocol for the uniform kpartition problem requires Ω(k) states to indicate a group, the space complexity of the proposed protocol is asymptotically optimal.

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“…The uniform k-partition problem and a similar problem have been considered in [16,25,29,30]. Lamani et al [25] studied a group composition problem, which aims to divide a population into groups of designated sizes.…”

Section: Related Workmentioning

confidence: 99%

Uniform Partition in Population Protocol Model under Weak Fairness

Yasumi,

Ooshita,

Inoue

2019

Preprint

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We focus on a uniform partition problem in a population protocol model. The uniform partition problem aims to divide a population into k groups of the same size, where k is a given positive integer. In the case of k = 2 (called uniform bipartition), a previous work clarified space complexity under various assumptions: 1) an initialized base station (BS) or no BS, 2) weak or global fairness, 3) designated or arbitrary initial states of agents, and 4) symmetric or asymmetric protocols, except for the setting that agents execute a protocol from arbitrary initial states under weak fairness in the model with an initialized base station. In this paper, we clarify the space complexity for this remaining setting. In this setting, we prove that P states are necessary and sufficient to realize asymmetric protocols, and that P+1 states are necessary and sufficient to realize symmetric protocols, where P is the known upper bound of the number of agents. From these results and the previous work, we have clarified the solvability of the uniform bipartition for each combination of assumptions. Additionally, we newly consider an assumption on a model of a non-initialized BS and clarify solvability and space complexity in the assumption. Moreover, the results in this paper can be applied to the case that k is an arbitrary integer (called uniform k-partition).

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Realization of Periodic Functions by Self-stabilizing Population Protocols with Synchronous Handshakes

Cited by 6 publications

References 9 publications

Space-Optimal Population Protocols for Uniform Bipartition Under Global Fairness

Space-Optimal Population Protocols for Uniform Bipartition Under Global Fairness

A Population Protocol for Uniform k-partition under Global Fairness

Uniform Partition in Population Protocol Model under Weak Fairness

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