Running time of the drilling algorithm

Determine how the running time of the veering-triangulation drilling algorithm depends on the number n of tetrahedra in the input veering triangulation and the length k of the input flow cycle.

Background

The paper gives a complete terminating algorithm for constructing a veering parent but does not analyze its computational complexity. Such an analysis would require bounds on the adapted continent and on the number and size of expansions performed during the algorithm.

References

Given a veering triangulation $V$ with $n$ tetrahedra and a flow cycle $$ of length $k$, how does the running time of the algorithm in Figure~\ref{fig:flowchart} depend on $n$ and $k$?

— Drilling veering triangulations with applications to pseudo-Anosov flows  (2610.12302 - Parlak et al., 8 Oct 2026) in Section 6.1, Question 6.1 (subsection Running time; no label provided)