A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916717317324800 |
|---|---|
| author | Austin, Henry Berenbrink, Petra Friedetzky, Tom Götte, Thorsten Hintze, Lukas |
| author_facet | Austin, Henry Berenbrink, Petra Friedetzky, Tom Götte, Thorsten Hintze, Lukas |
| contents | We consider the problem of self-stabilizing leader election in the population model by Angluin, Aspnes, Diamadi, Fischer, and Peralta (JDistComp '06). The population model is a well-established and powerful model for asynchronous, distributed computation with a large number of applications. For self-stabilizing leader election, the population of $n$ anonymous agents, interacting in uniformly random pairs, must stabilize with a single leader from any possible initial configuration.
The focus of this paper is to develop time-efficient self-stabilizing protocols whilst minimizing the number of states. We present a parametrized protocol, which, for a suitable setting, achieves the asymptotically optimal time $O(\log n)$ using $2^{O(n^2\log n)}$ states (throughout the paper, ``time'' refers to ``parallel time'', i.e., the number of pairwise interactions divided by $n$). This is a significant improvement over the previously best protocol Sublinear-Time-SSR due to Burman, Chen, Chen, Doty, Nowak, Severson, and Xu (PODC '21), which requires $2^{O(n^{\log n}\log n)}$ states for the same time bound. In general, for $1\le r\le n/2$, our protocol requires $2^{O(r^2\log{n})}$ states and stabilizes in time $O((n\log{n})/r)$, w.h.p.; the above result is achieved for $r=Θ(n)$. For $r=\log^2n$ our protocol requires only sub-linear time using only $2^{O(\log^3 n)}$ states, resolving an open problem stated in that paper. Sublinear-Time-SSR requires $O(\log n\cdot n^{1/(H+1)})$ time using $2^{Θ(n^H) \cdot \log n}$ states for all $1\le H\leΘ(\log n)$.
Similar to previous works, it solves leader election by assigning a unique rank from $1$ through $n$ to each agent. The principal bottleneck for self-stabilizing ranking usually is to detect if there exist agents with the same rank. One of our main conceptual contributions is a novel technique for collision detection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols Austin, Henry Berenbrink, Petra Friedetzky, Tom Götte, Thorsten Hintze, Lukas Distributed, Parallel, and Cluster Computing We consider the problem of self-stabilizing leader election in the population model by Angluin, Aspnes, Diamadi, Fischer, and Peralta (JDistComp '06). The population model is a well-established and powerful model for asynchronous, distributed computation with a large number of applications. For self-stabilizing leader election, the population of $n$ anonymous agents, interacting in uniformly random pairs, must stabilize with a single leader from any possible initial configuration. The focus of this paper is to develop time-efficient self-stabilizing protocols whilst minimizing the number of states. We present a parametrized protocol, which, for a suitable setting, achieves the asymptotically optimal time $O(\log n)$ using $2^{O(n^2\log n)}$ states (throughout the paper, ``time'' refers to ``parallel time'', i.e., the number of pairwise interactions divided by $n$). This is a significant improvement over the previously best protocol Sublinear-Time-SSR due to Burman, Chen, Chen, Doty, Nowak, Severson, and Xu (PODC '21), which requires $2^{O(n^{\log n}\log n)}$ states for the same time bound. In general, for $1\le r\le n/2$, our protocol requires $2^{O(r^2\log{n})}$ states and stabilizes in time $O((n\log{n})/r)$, w.h.p.; the above result is achieved for $r=Θ(n)$. For $r=\log^2n$ our protocol requires only sub-linear time using only $2^{O(\log^3 n)}$ states, resolving an open problem stated in that paper. Sublinear-Time-SSR requires $O(\log n\cdot n^{1/(H+1)})$ time using $2^{Θ(n^H) \cdot \log n}$ states for all $1\le H\leΘ(\log n)$. Similar to previous works, it solves leader election by assigning a unique rank from $1$ through $n$ to each agent. The principal bottleneck for self-stabilizing ranking usually is to detect if there exist agents with the same rank. One of our main conceptual contributions is a novel technique for collision detection. |
| title | A Space-Time Trade-off for Fast Self-Stabilizing Leader Election in Population Protocols |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2505.01210 |