Improving Efficiency in Near-State and State-Optimal Self-Stabilising Leader Election Population Protocols
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arXiv
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| Format: | Preprint |
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2025
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| author | Gąsieniec, Leszek Grodzicki, Tytus Stachowiak, Grzegorz |
| author_facet | Gąsieniec, Leszek Grodzicki, Tytus Stachowiak, Grzegorz |
| contents | We investigate leader election problem via ranking within self-stabilising population protocols. In this scenario, the agent's state space comprises $n$ rank states and $x$ extra states. The initial configuration of $n$ agents consists of arbitrary arrangements of rank and extra states, with the objective of self-ranking. Specifically, each agent is tasked with stabilising in a unique rank state silently, implying that after stabilisation, each agent remains in its designated state indefinitely.
In this paper, we present several new self-stabilising ranking protocols, greatly enriching our comprehension of these intricate problems. All protocols ensure self-stabilisation time with high probability (whp), defined as $1-n^{-η},$ for a constant $η>0.$ We delve into three scenarios, from which we derive stable (always correct), either state-optimal or almost state-optimal, silent ranking protocols that self-stabilise within a time frame of $o(n^2)$ whp, including:
- Utilising a novel concept of an agent trap, we derive a state-optimal ranking protocol that achieves self-stabilisation in time $O(min(kn^{3/2},n^2\log^2 n)),$ for any $k$-distant starting configuration.
- Furthermore, we show that the incorporation of a single extra state ($x=1$) ensures a ranking protocol that self-stabilises in time $O(n^{7/4}\log^2 n)=o(n^2)$, regardless of the initial configuration.
- Lastly, we show that extra $x=O(\log n)$ states admit self-stabilising ranking with the best currently known stabilisation time $O(n\log n)$, when whp and $x=O(\log n)$ guarantees are imposed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01227 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improving Efficiency in Near-State and State-Optimal Self-Stabilising Leader Election Population Protocols Gąsieniec, Leszek Grodzicki, Tytus Stachowiak, Grzegorz Distributed, Parallel, and Cluster Computing F.2.2 We investigate leader election problem via ranking within self-stabilising population protocols. In this scenario, the agent's state space comprises $n$ rank states and $x$ extra states. The initial configuration of $n$ agents consists of arbitrary arrangements of rank and extra states, with the objective of self-ranking. Specifically, each agent is tasked with stabilising in a unique rank state silently, implying that after stabilisation, each agent remains in its designated state indefinitely. In this paper, we present several new self-stabilising ranking protocols, greatly enriching our comprehension of these intricate problems. All protocols ensure self-stabilisation time with high probability (whp), defined as $1-n^{-η},$ for a constant $η>0.$ We delve into three scenarios, from which we derive stable (always correct), either state-optimal or almost state-optimal, silent ranking protocols that self-stabilise within a time frame of $o(n^2)$ whp, including: - Utilising a novel concept of an agent trap, we derive a state-optimal ranking protocol that achieves self-stabilisation in time $O(min(kn^{3/2},n^2\log^2 n)),$ for any $k$-distant starting configuration. - Furthermore, we show that the incorporation of a single extra state ($x=1$) ensures a ranking protocol that self-stabilises in time $O(n^{7/4}\log^2 n)=o(n^2)$, regardless of the initial configuration. - Lastly, we show that extra $x=O(\log n)$ states admit self-stabilising ranking with the best currently known stabilisation time $O(n\log n)$, when whp and $x=O(\log n)$ guarantees are imposed. |
| title | Improving Efficiency in Near-State and State-Optimal Self-Stabilising Leader Election Population Protocols |
| topic | Distributed, Parallel, and Cluster Computing F.2.2 |
| url | https://arxiv.org/abs/2502.01227 |