发表机构
The University of Osaka（大阪大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在CONGEST-KT₁模型中提出新型分布式MST算法，突破二次时间-消息权衡障碍，特定参数设置下达轮次最优并改进消息界，还衍生出低消息相关算法。
AI 中文摘要
我们提出了一种在CONGEST-KT₁模型中计算最小生成树（MST）的新型分布式算法，该模型中消息被限制为O(log n)位，且每个顶点初始时已知其邻居的标识符。我们的算法呈现出两参数的时间-消息权衡：对于任意0≤λ≤κ≤1/2，其运行时间为Õ(n^λD_G + n^{1−κ−λ} + n^{1−2κ+λ} + n^{1/2})轮，使用的消息量为Õ(min{m, n^{1+κ}})，其中n、m和D_G分别为顶点数、边数和网络直径。特别地，当设置(κ, λ)=(1/3, 1/6)时，可得到一种MST算法，其运行时间为Õ(n^{1/2} + n^{1/6}D_G)轮，仅使用Õ(n^{4/3})条消息。在D_G=O(n^{1/3})的温和假设下，该算法达到了轮次最优，同时改进了此前已知的Õ(n^{3/2})消息界。更广泛地说，我们的算法打破了二次时间-消息权衡障碍（轮次·消息=Ω̃(n²)），而此前CONGEST-KT₁模型中的所有MST算法均未能克服这一障碍，且在几乎整个直径D_G范围内均实现了这一突破。作为副产品，我们还得到了新的低消息广播、生成树和领导者选举算法。
英文摘要
We present a new distributed algorithm for computing a minimum spanning tree (MST) in the \textsf{CONGEST-KT$_{1}$} model, where messages are limited to $O(\log n)$ bits and each vertex initially knows the identifiers of its neighbors. Our algorithm exposes a two-parameter time--message trade-off: for any $0 \leq λ\leq κ\leq 1/2$, it runs in $\tilde{O}(n^λD_G + n^{1 - κ- λ} + n^{1 - 2κ+ λ} + n^{1/2})$ rounds and uses $\tilde{O}(\min\{m, n^{1 + κ}\})$ messages, where $n$, $m$, and $D_G$ are the number of vertices, edges, and thenetwork diameter, respectively. In particular, setting $(κ, λ) = (1/3, 1/6)$ yields an MST algorithm running in $\tilde{O}(n^{1/2} + n^{1/6}D_G)$ rounds with only $\tilde{O}(n^{4/3})$ messages. Under the mild assumption $D_G = O(n^{1/3})$, this is round-optimal while improving the best known message bound of $\tilde{O}(n^{3/2})$. More broadly, our algorithm breaks the quadratic time--message trade-off barrier $\mathrm{\# rounds} \cdot \mathrm{\# messages} = \tildeΩ(n^2)$, which no previous MST algorithm in the \textsf{CONGEST-KT$_{1}$} model has been able to overcome, and it does so for almost the entire range of the diameter $D_G$. As a byproduct, we also obtain new low-message broadcast, spanning-tree, and leader-election algorithms.
