AI 中文总结
本文引入统一端口模型，设计高效自稳定算法解决一般图上多种局部对称性破缺问题，如最大独立集等，此前虽在更强模型中有相关研究，但此为首次在真正统一模型中证明此类算法存在。
AI 中文摘要
我们引入了一种称为“统一端口”模型的分布式计算模型。在该模型中运行的算法由与输入图的端口（即半边）相关联的局部自动机定义。统一端口模型的关键在于每个图的每个端口都有一个单一的固定大小有限自动机，使其真正统一。此外，新模型明确支持为图的（半）边分配（输入和）输出标签，便于自然地表述诸如最大匹配和无汇定向等（半）边标记问题，而这些问题超出了先前以节点为中心的真正统一分布式计算模型的表达范围。本文的主要技术贡献是设计了高效（即运行时间为多对数）的自稳定统一端口算法，用于在一般图上解决各种基本的局部对称性破缺问题，包括最大独立集、最大匹配、无汇定向和最大节点/边k着色。虽然在更强的计算模型中已经广泛研究了用于局部对称性破缺问题的高效自稳定算法，但我们的工作首次证明了在真正统一的模型中存在这样的算法。
英文摘要
We introduce a distributed computational model referred to as the \emph{uniform port} model. An algorithm operating in this model is defined by means of local automata associated with the ports (a.k.a.\ half-edges) of the input graph. The crux of the uniform port model is that a single constant-size finite automaton is hosted by every port of every graph, making the model \emph{truly uniform}. Moreover, since the new model explicitly supports the assignment of (input and) output labels to the graph's (half-)edges, it facilitates natural formulations of (half-)edge-labeling problems such as maximal matching and sinkless orientation, which are outside the expressivity scope of prior node-centric truly uniform distributed computational models. The main technical contribution of this paper is the design of efficient (i.e., with poly-logarithmic runtime) \emph{self-stabilizing} uniform port algorithms, operating on general graphs, for various fundamental local symmetry breaking problems, including maximal independent set, maximal matching, sinkless orientation, and maximal node/edge $k$-coloring. While efficient self-stabilizing algorithms for local symmetry breaking problems have been extensively studied in stronger computational models, our work is the first to demonstrate the existence of such algorithms in a truly uniform model.
CommentsAccepted to the 40th International Symposium on Distributed Computing (DISC), 2026
