Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909601537982464 |
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| author | Breitkopf, Tom-Lukas Dallot, Julien El-Hayek, Antoine Schmid, Stefan |
| author_facet | Breitkopf, Tom-Lukas Dallot, Julien El-Hayek, Antoine Schmid, Stefan |
| contents | This paper revisits a fundamental distributed computing problem in the population protocol model.
Provided $n$ agents each starting with an input color in $[k]$, the relative majority problem asks to find the predominant color.
In the population protocol model, at each time step, a scheduler selects two agents that first learn each other's states and then update their states based on what they learned.
We present the \textsc{Circles} protocol that solves the relative majority problem with $k^3$ states. It is always-correct under weakly fair scheduling.
Not only does it improve upon the best known upper bound of $O(k^7)$, but it also shows a strikingly simpler design inspired by energy minimization in chemical settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols Breitkopf, Tom-Lukas Dallot, Julien El-Hayek, Antoine Schmid, Stefan Distributed, Parallel, and Cluster Computing This paper revisits a fundamental distributed computing problem in the population protocol model. Provided $n$ agents each starting with an input color in $[k]$, the relative majority problem asks to find the predominant color. In the population protocol model, at each time step, a scheduler selects two agents that first learn each other's states and then update their states based on what they learned. We present the \textsc{Circles} protocol that solves the relative majority problem with $k^3$ states. It is always-correct under weakly fair scheduling. Not only does it improve upon the best known upper bound of $O(k^7)$, but it also shows a strikingly simpler design inspired by energy minimization in chemical settings. |
| title | Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2505.02785 |