AI 中文总结
针对同步完全n节点图在CONGEST模型下，提出一种带可调分支参数ℓ的随机树相交领导者选举算法，实现时间与每节点消息复杂度的灵活权衡，总消息复杂度严格亚线性，适配不同带宽需求。
AI 中文摘要
我们针对同步完全n节点图在CONGEST模型下提出了一种随机领导者选举算法，该算法在时间复杂度和每节点消息复杂度之间引入了高度可调的权衡。通过调整单个分支参数ℓ，系统设计者可将算法负担在执行时间与每节点消息复杂度之间平滑转换，同时保持严格的亚线性总消息复杂度O(√n log^1.5 n)。我们通过利用动态截断的ℓ叉树扩展结合新颖的“静默脉冲”验证机制实现这一目标。通过强制扩展形成精确体积的几乎完全树，节点可安全聚合拓扑权重而不超过亚线性消息边界。具体而言，我们的算法实现了O(log_ℓ √(n log n))的时间（轮次）复杂度和O(ℓ)的每节点消息复杂度。这种灵活性使带宽受限的网络能以最小O(1)的每节点负担运行，而高带宽环境可将选举压缩至O(1)时间单位。
英文摘要
We present a randomized leader election algorithm for synchronous complete $n$-node graphs in the \textsf{CONGEST} model that introduces a highly tunable trade-off between time complexity and the per-node message complexity. By adjusting a single branching parameter, $\ell$, system designers can smoothly shift the algorithmic burden from execution time to per-node message complexity, all while maintaining a strictly sublinear total message complexity of $O(\sqrt{n} \log^{1.5} n)$. We achieve this by utilizing dynamically truncated $\ell$-ary tree expansions coupled with a novel ``silent pulse'' verification mechanism. By forcing the expansions to form exact-volume almost-complete trees, nodes can safely aggregate topological weights without overshooting the sublinear message bounds. Specifically, our algorithm achieves $O(\log_\ell \sqrt{n \log n})$ time (round) complexity and $O(\ell)$ per-node message complexity. This flexibility allows networks with tight bandwidth constraints to operate with a minimal $O(1)$ per-node burden, while high-bandwidth environments can collapse the election into $O(1)$ time units.
CommentsFull version of a DISC 2026 paper
