Algorithmic complexity of list-distance consistency on broader tree classes

Investigate the algorithmic complexity of determining the list-distance consistency number ldc(T) for trees, including the development of specialized algorithms for caterpillars and related classes of trees.

Background

The paper establishes structural results for list-distance consistent vertices in trees and uses them to determine ldc(T) for complete k-ary trees and all spiders. These results suggest that the path structure theorem may support analogous analyses for broader classes of trees.

The computational complexity of determining ldc(T), together with specialized algorithms for caterpillars and related tree classes, is identified as work not undertaken in the paper and left for separate investigation.