Minimal Leader Set for Controllability of k-distant Trees

TL;DR

This paper introduces the concept of Minimum Perfect Critical Sets (MPCS) for k-distant trees, providing an algorithm to find minimal leader sets with high probability, advancing network controllability understanding.

Contribution

It proposes MPCS as a new concept for controllability, identifies four types of MPCS in k-distant trees, and develops an effective algorithm for minimal leader set selection.

Findings

Four types of MPCS identified in k-distant trees

Algorithm achieves over 98% success in finding minimal leader sets

Numerical characteristics of minimal leader sets analyzed

Abstract

Minimal controllability problem plays an important role in the field of network control. A New concept-Minimum Perfect Critical Set (MPCS)is proposed. Four different MPCSs were found for k-distant tree graphs. Based on this concept of MPCS, an algorithm for finding the minimal leader set is provided. Numerical experiments show that these theories enable the algorithm to find a minimal leader set with a probability of more than 0.98. Further, some other numerical characteristics of the minimal leader set of k-distant trees were found.