Determine the complexity and approximability of the remaining parameters

Determine the computational complexity of computing the parameters denoted by the power-AT index and the power-cocomparability index, and establish whether non-trivial inapproximability results hold for these hard-to-compute parameters.

Background

The paper states that several parameters, including path-length and related domination and distortion parameters, are NP-hard to compute exactly, whereas BFS-layering parameters and other quantities are computable in polynomial time and provide constant-factor approximations. The exact complexity and possible inapproximability of the two parameters identified in the concluding question are left unresolved.

References

What is the complexity of computing $(G),$ $(G)}$? Can non-trivial inapproximability results be obtained for those hard to compute parameters?

— Graph parameters that are coarsely equivalent to path-length  (2503.05661 - Dragan et al., 7 Mar 2025) in Section 5, “Concluding remarks and open questions”