Abstract:We propose a self-stabilizing leader election (SS-LE) protocol on ring networks in the population protocol model. Given an integer $\psi$ satisfying $\log n \le \psi \le \log n+O(1)$, where $n$ is the population size, the proposed protocol reaches a safe configuration within $O(n^2 \log n)$ steps with high probability from any initial configuration, and thereafter preserves the same unique leader forever. Since no protocol solves SS-LE in $o(n^2)$ steps with high probability, the convergence time is near-optimal, with only an $O(\log n)$ multiplicative gap. The proposed protocol uses only $\mathit{polylog}(n)$ states. Two state-of-the-art protocols are known for SS-LE on ring networks. The first protocol uses a polynomial number of states and solves SS-LE in $O(n^2)$ steps, whereas the second protocol requires super-exponential time but uses only a constant number of states. Our proposed protocol provides a useful middle ground between these two approaches.
From: Yuichi Sudo [view email]
[v1]
Mon, 15 May 2023 06:21:47 UTC (115 KB)
[v2]
Sun, 16 Aug 2026 09:28:07 UTC (92 KB)
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