6 citations · 11 across the 10 of their papers we have counts for
14 papers · 1 filter
Sketching Persistence Diagrams
Donald R. Sheehy, Siddharth Sheth
Given a persistence diagram with points, we give an algorithm that produces a sequence of persistence diagrams converging in bottleneck distance to the input diagram, the $…
A Sparse Delaunay Filtration
Donald R. Sheehy
We show how a filtration of Delaunay complexes can be used to approximate the persistence diagram of the distance to a point set in . Whereas the full Delaunay complex can be…
Randomized Incremental Construction of Net-Trees
Mahmoodreza Jahanseir, Donald R. Sheehy
Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct…
Adaptive Metrics for Adaptive Samples
Nicholas J. Cavanna, Donald R. Sheehy
In this paper we consider adaptive sampling's local-feature size, used in surface reconstruction and geometric inference, with respect to an arbitrary landmark set rather than the…
Exact Computation of a Manifold Metric, via Lipschitz Embeddings and Shortest Paths on a Graph
Timothy Chu, Gary Miller, Donald Sheehy
Data-sensitive metrics adapt distances locally based the density of data points with the goal of aligning distances and some notion of similarity. In this paper, we give the first…
Supporting Ruled Polygons
Nicholas J. Cavanna, Marc Khoury, Donald R. Sheehy
We explore several problems related to ruled polygons. Given a ruling of a polygon , we consider the Reeb graph of induced by the ruling. We define the Reeb complexity of $P…
Approximating the Simplicial Depth
Peyman Afshani, Donald R. Sheehy, Yannik Stein
Let be a set of points in -dimensions. The simplicial depth, of a point is the number of -simplices with vertices in that contain in their convex…
A Geometric Perspective on Sparse Filtrations
Nicholas J. Cavanna, Mahmoodreza Jahanseir, Donald R. Sheehy
We present a geometric perspective on sparse filtrations used in topological data analysis. This new perspective leads to much simpler proofs, while also being more general, applyi…
Approximating Nearest Neighbor Distances
Michael B. Cohen, Brittany Terese Fasy, Gary L. Miller +3
Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes t…
Efficient and Robust Persistent Homology for Measures
Mickael Buchet, Frederic Chazal, Steve Y. Oudot +1
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is ro…
A Fast Algorithm for Well-Spaced Points and Approximate Delaunay Graphs
Gary L. Miller, Donald R. Sheehy, Ameya Velingker
We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an a…
A New Approach to Output-Sensitive Voronoi Diagrams and Delaunay Triangulations
Gary L. Miller, Donald R. Sheehy
We describe a new algorithm for computing the Voronoi diagram of a set of points in constant-dimensional Euclidean space. The running time of our algorithm is $O(f \log n \log…
Linear-Size Approximations to the Vietoris-Rips Filtration
Donald R. Sheehy
The Vietoris-Rips filtration is a versatile tool in topological data analysis. It is a sequence of simplicial complexes built on a metric space to add topological structure to an o…
Compatible Triangulations and Point Partitions by Series-Triangular Graphs
Jeff Danciger, Satyan L. Devadoss, Don Sheehy
We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points…