在离散空间中求地形：度量维数及其应用综述
Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and its Applications
摘要：
图的度量维度是基于最短路径距离唯一识别所有其他节点所需的最小节点数量。度量维数的应用包括发现网络中传播的来源，规范标记图，以及在低维欧几里得空间中嵌入符号数据。本调查给出了一个自包含的介绍度量尺寸和概述的典型结果和应用。我们讨论了一般图的度量维数的近似方法，以及确定性和随机图族的具体界限和渐近行为。我们的结论与相关的概念和未来的工作方向。
英文摘要：
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network, canonically labeling graphs, and embedding symbolic data in low-dimensional Euclidean spaces. This survey gives a self-contained introduction to metric dimension and an overview of the quintessential results and applications. We discuss methods for approximating the metric dimension of general graphs, and specific bounds and asymptotic behavior for deterministic and random families of graphs. We conclude with related concepts and directions for future work.
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