Time-Optimal Self-Stabilizing Leader Election on Rings in Population Protocols

Yokota, Daisuke; Sudo, Yuichi; Masuzawa, Toru

doi:10.1587/transfun.2020eap1125

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…At the same time, Beauquier, Blanchard and Burman [13] showed that there exists a constant-state protocol that solves stable leader election as long as self-stabilization is not required. Subsequently, research on leader election in the population model has largely fallen into two categories: (1) work that tries to understand computational complexity and space-time complexity trade-offs of leader election under uniform random pairwise interactions on the clique [4,14,15,24,27,30,31,42,44,45], and (2) work that aims to understand in which interaction graphs and under what model assumptions leader election can be solved in, e.g., a fault-tolerant manner [11,13,18,19,43,[46][47][48].…”

Section: Prior Work On Leader Election In the Population Modelmentioning

confidence: 99%

Near-Optimal Leader Election in Population Protocols on Graphs

Alistarh¹,

Rybicki²,

Sasha³

2022

Preprint

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In the stochastic population protocol model, we are given a connected graph with nodes, and in every time step, a scheduler samples an edge of the graph uniformly at random and the nodes connected by this edge interact. A fundamental task in this model is stable leader election, in which all nodes start in an identical state and the aim is to reach a configuration in which (1) exactly one node is elected as leader and (2) this node remains as the unique leader no matter what sequence of interactions follows. On cliques, the complexity of this problem has recently been settled: time-optimal protocols stabilize in Θ( log ) expected steps using Θ(log log ) states, whereas protocols that use (1) states require Θ( 2 ) expected steps.In this work, we investigate the complexity of stable leader election on general graphs. We provide the first non-trivial time lower bounds for leader election on general graphs, showing that, when moving beyond cliques, the complexity landscape of leader election becomes very diverse: the time required to elect a leader can range from (1) to Θ( 3 ) expected steps. On the upper bound side, we first observe that there exists a protocol that is time-optimal on many graph families, but uses polynomially-many states. In contrast, we give a near-time-optimal protocol that uses only (log 2 ) states that is at most a factor log slower. Finally, we show that the constant-state protocol of Beauquier et al. [OPODIS 2013] is at most a factor log slower than the fast polynomial-state protocol.Moreover, among constant-state protocols, this protocol has near-optimal average case complexity on dense random graphs.

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Section: Prior Work On Leader Election In the Population Modelmentioning

confidence: 99%

Near-Optimal Leader Election in Population Protocols on Graphs

Alistarh¹,

Rybicki²,

Sasha³

2022

Preprint

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“…Self-stabilizing leader election has also been well studied [4,37,39,19,20,40,42,25,7,13,14,35]. In the self-stabilizing setting, we do not assume that all agents are initialized at the beginning of an execution.…”

Section: Related Workmentioning

confidence: 99%

“…Unfortunately, the self-stabilizing leader election cannot be solved in the standard model [4]. Thus, this problem has been considered (i) by assuming that the agents have global knowledge such as the exact number of agents [14,13,40], (ii) by assuming the existence of oracles [25,7], (iii) by slightly relaxing the requirement of self-stabilization [37,39,35], or (iv) by assuming a specific topology of the population such as rings [4,19,20,42].…”

Section: Related Workmentioning

confidence: 99%

“…The goal is to design a protocol, such that, after a sufficient number of interactions, the population always converges to a configuration with a unique leader. The leader election problem has received a large amount of attention in the population protocol literature [5,4,3,1,2,26,27,38,37,39,19,20,40,42,25,7,13,14,35] and thus makes the perfect case study for our model.…”

Section: Introductionmentioning

confidence: 99%

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Smoothed Analysis of Population Protocols

Schwartzman,

Sudo

2021

Preprint

Self Cite

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In this work, we initiate the study of smoothed analysis of population protocols. We consider a population protocol model where an adaptive adversary dictates the interactions between agents, but with probability p every such interaction may change into an interaction between two agents chosen uniformly at random. That is, p-fraction of the interactions are random, while (1 − p)-fraction are adversarial. The aim of our model is to bridge the gap between a uniformly random scheduler (which is too idealistic) and an adversarial scheduler (which is too strict).We focus on the fundamental problem of leader election in population protocols. We show that, for a population of size n, the leader election problem can be solved in O(p −2 n log 3 n) steps with high probability, using O((log 2 n) • (log(n/p))) states per agent, for all values of p ≤ 1. Although our result does not match the best known running time of O(n log n) for the uniformly random scheduler (p = 1), we are able to present a smooth transition between a running time of O(n polylog n) for p = 1 and an infinite running time for the adversarial scheduler (p = 0), where the problem cannot be solved. The key technical contribution of our work is a novel phase clock algorithm for our model. This is a key primitive for much-studied fundamental population protocol algorithms (leader election, majority), and we believe it is of independent interest.

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Complete Graph Identification in Population Protocols

Kanaya,

Sudo

2024

Lecture Notes in Computer Science

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Time-Optimal Self-Stabilizing Leader Election on Rings in Population Protocols

Cited by 4 publications

References 22 publications

Near-Optimal Leader Election in Population Protocols on Graphs

Near-Optimal Leader Election in Population Protocols on Graphs

Smoothed Analysis of Population Protocols

Complete Graph Identification in Population Protocols

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