We extend the definition of persistence diagram to a larger setting, introduce the notions of discretization of a persistence module and associated pixelization map, and show how to interpolate between persistence modules, thereby lending a more analytic character to this otherwise algebraic setting.Expand

We present a novel algorithm that takes as an input a data set, and outputs a metric graph that is homeomorphic to the underlying metric graph and has bounded distortion of distances.Expand

We present the main algorithmic and design choices that have been made to represent complexes and compute persistent homology in the Gudhi library.Expand

We prove that the set of lines tangent to four possibly intersecting convex polyhedra in $\mathbb{R}^3$ with a total of $n$ edges consists of $\Theta(n^2k^2)$ connected components in the worst case.Expand

We establish convergence rates of persistence diagrams associated to data randomly sampled from any compact metric space to a well defined limit diagram encoding the topological features of the support of the measure.Expand

Given a family of k disjoint connected polygonal sites of total complexity n, we consider the farthest-site Voronoi diagram of these sites, and give an O(n log3 n) time algorithm to compute it.Expand

We show that for planar convex sets, the number of facets of the convex hull of $n$ points chosen uniformly and independently in a convex body is asymptotically increasing.Expand

We consider the farthest-site Voronoi diagram of k disjoint connected polygonal sites in general position and of total complexity n, and give an O(nlog^3n) time algorithm to compute it.Expand