Metric Dimension

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

Abstract: metric dimension of a graph is the smallest number of vertices from which the vector of distances to every vertex in the graph is unique. It may be regarded as a generalization of the concept of trilateration in the two-dimensional real plane, the idea underpinning the Global Positioning System (GPS). Contents 1 Definition 2 Brute force calculation 3 Complexity and approximation algorithms 4 Metric dimension of specific graph families 5 Applications 6 Acknowledgements 7