Before revision:  Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices,  for which we show that no computation is required as they are introduced in the hierarchy.
After revision:  Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are vertices that have no impact on the topological description of the data and for which we show that no computation is required as they are introduced in the hierarchy.