The double-exponential lower bounds obtained using the authors' technique have significant applications and implications in the context of network design and monitoring problems. These lower bounds provide insights into the inherent computational complexity of solving Metric Dimension, Strong Metric Dimension, and Geodetic Set on graphs with bounded diameter or treewidth.
In network design, the lower bounds highlight the challenges in efficiently solving metric-based graph problems, even on restricted graph classes. They emphasize the computational hardness of finding optimal solutions for these problems, especially when considering the interplay between structural parameters like treewidth and vertex cover.
Furthermore, in network monitoring, the double-exponential lower bounds shed light on the limitations of algorithmic approaches for resolving Metric Dimension, Strong Metric Dimension, and Geodetic Set. These bounds serve as a benchmark for evaluating the efficiency of algorithms and provide guidance for developing improved computational methods for network monitoring applications.