在离散空间中求地平面：度量维数及其应用综述

IF 10.8 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Review Pub Date : 2023-11-07 DOI:10.1137/21m1409512

Richard C. Tillquist, Rafael M. Frongillo, Manuel E. Lladser

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引用次数: 28

摘要

SIAM评论，第65卷，第4期，第919-962页，2023年11月。图的度量维度是根据最短路径距离唯一识别所有其他节点所需的最小节点数。度量维的应用包括发现网络中传播的来源，规范地标记图，以及在低维欧几里得空间中嵌入符号数据。这项调查对度量维度进行了独立的介绍，并概述了典型的结果和应用。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特定界和渐近行为。最后，我们提出了相关的概念和未来工作的方向。

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Getting the Lay of the Land in Discrete Space: A Survey of Metric Dimension and Its Applications

SIAM Review, Volume 65, Issue 4, Page 919-962, November 2023.
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes uniquely based on shortest path distances. 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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来源期刊

SIAM Review 数学-应用数学

CiteScore

16.90

自引率

0.00%

发文量

期刊介绍： Survey and Review feature papers that provide an integrative and current viewpoint on important topics in applied or computational mathematics and scientific computing. These papers aim to offer a comprehensive perspective on the subject matter. Research Spotlights publish concise research papers in applied and computational mathematics that are of interest to a wide range of readers in SIAM Review. The papers in this section present innovative ideas that are clearly explained and motivated. They stand out from regular publications in specific SIAM journals due to their accessibility and potential for widespread and long-lasting influence.