Throttling for Metric Dimension and Its Variants

Authors

• Boris Brimkov, Slippery Rock University
• Peter Diao, Princeton University
• Jesse Geneson, San Jose State UniversityFollow
• Carolyn Reinhart, Swarthmore College
• Shen Fu Tsai, National Central University
• William Wang, Massachusetts Institute of Technology
• Kyle Worley, San Jose State UniversityFollow

Publication Date

5-22-2026

Document Type

Article

Publication Title

Theoretical Computer Science

Volume

1073

DOI

10.1016/j.tcs.2026.115903

Abstract

Metric dimension is a graph parameter that has been applied to robot navigation and finding low-dimensional vector embeddings. Throttling entails minimizing the sum of two available resources when solving certain graph problems. In this paper, we introduce throttling for metric dimension, edge metric dimension, and mixed metric dimension. In the context of vector embeddings, metric dimension throttling finds a low-dimensional, low-magnitude embedding with integer coordinates. We show that computing the throttling number is NP-hard for all three variants. We give formulas for the throttling numbers of special families of graphs, and characterize graphs with extremal throttling numbers. We also prove that the minimum possible throttling number of a graph of order n is [Formula presented], while the minimum possible throttling number of a tree of order n is Θ(n^1/3) or Θ(n^1/2) depending on the variant of metric dimension.

Keywords

Edge metric dimension, Metric dimension, Mixed metric dimension, Throttling

Department

Mathematics and Statistics

Recommended Citation

Boris Brimkov, Peter Diao, Jesse Geneson, Carolyn Reinhart, Shen Fu Tsai, William Wang, and Kyle Worley. "Throttling for Metric Dimension and Its Variants" Theoretical Computer Science (2026). https://doi.org/10.1016/j.tcs.2026.115903