Efficient computation of active vertices

Develop a simple method for computing all active vertices on the cycle of an optimal lollipop under the paper’s recursive active-path construction.

Background

Active vertices are endpoints of Hamiltonian paths generated recursively from the cycle of a lollipop. The proof uses the existence of sufficiently many active vertices, while the algorithmic discussion notes that there may be exponentially many active paths and therefore proposes tracking only enough paths to obtain the required number of distinct endpoints. The authors nevertheless ask whether all active vertices of an optimal lollipop can be computed simply.