Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of \({\tilde{\Omega }}(\sqrt{n} + D)\) rounds for several global problems, where n denotes the number of nodes and D the diameter of the input graph. Because such a lower bound is derived from special “hard-core” instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts was initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. In particular, given a graph class \({\mathcal {C}}\), an f-round algorithm for constructing shortcuts of quality q for any instance in \({\mathcal {C}}\) results in \({\tilde{O}}(q + f)\)-round algorithms for solving several fundamental graph problems such as minimum spanning tree and minimum cut, for \({\mathcal {C}}\). The main interest on this line is to identify the graph classes allowing the shortcuts that are efficient in the sense of breaking \({\tilde{O}}(\sqrt{n}+D)\)-round general lower bounds. In this study, we consider the relationship between the quality of low-congestion shortcuts and the following four major graph parameters: doubling dimension, chordality, diameter, and clique-width. The key ingredient of the upper-bound side is a novel shortcut construction technique known as short-hop extension, which might be of independent interest.

对于几个全局问题，标准 CONGEST 模型中的分布式图算法通常表现出\({\tilde{\Omega }}(\sqrt{n} + D)\)轮的时间复杂度下界，其中n表示节点和D输入图的直径。因为这样的下界来自特殊的“核心”实例，所以它不一定适用于特定的流行图类，例如平面图。低拥塞捷径的概念由 Ghaffari 和 Haeupler [SODA2016] 提出，用于解决在受限网络拓扑中快速运行的 CONGEST 算法的设计问题。特别地，给定一个图类\({\mathcal {C}}\)，一个f- 为\({\mathcal {C}}\) 中的任何实例构造质量q 的捷径的轮算法导致\({\tilde{O}}(q + f)\) - 用于解决几个基本图的轮算法\({\mathcal {C}}\) 的最小生成树和最小割等问题。这一行的主要兴趣是识别允许在打破\({\tilde{O}}(\sqrt{n}+D)\)意义上有效的快捷方式的图类-round 一般下限。在本研究中，我们考虑了低拥塞捷径的质量与以下四个主要图形参数之间的关系：倍数维度、弦度、直径和团宽。上限侧的关键成分是一种称为短跳扩展的新型快捷方式构造技术，它可能具有独立的兴趣。