3 citations · 5 across the 5 of their papers we have counts for
9 papers
Improved Approximate Rips Filtrations with Shifted Integer Lattices and Cubical Complexes
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes is expensive because of a combinatorial explo…
Computational Complexity of the -Ham-Sandwich Problem
Man-Kwun Chiu, Aruni Choudhary, Wolfgang Mulzer
The classic Ham-Sandwich theorem states that for any measurable sets in , there is a hyperplane that bisects them simultaneously. An extension by Bárány, Hubard,…
No-dimensional Tverberg Theorems and Algorithms
Aruni Choudhary, Wolfgang Mulzer
Tverberg's theorem states that for any and any set of at least points in dimensions, we can partition into subse…
Improved Topological Approximations by Digitization
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Čech complexes are useful simplicial complexes for computing and analyzing topological features of data that lies in Euclidean space. Unfortunately, computing these complexes becom…
Delaunay simplices in diagonally distorted lattices
Aruni Choudhary, Arijit Ghosh
Delaunay protection is a measure of how far a Delaunay triangulation is from being degenerate. In this short paper we study the protection properties and other quality measures of…
Improved Approximate Rips Filtrations with Shifted Integer Lattices
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a co…
Polynomial-Sized Topological Approximations Using The Permutahedron
Aruni Choudhary, Michael Kerber, Sharath Raghvendra
Classical methods to model topological properties of point clouds, such as the Vietoris-Rips complex, suffer from the combinatorial explosion of complex sizes. We propose a novel t…
Local Doubling Dimension of Point Sets
Aruni Choudhary, Michael Kerber
We introduce the notion of t-restricted doubling dimension of a point set in Euclidean space as the local intrinsic dimension up to scale t. In many applications information is onl…
Approximate Cech Complexes in Low and High Dimensions
Michael Kerber, R. Sharathkumar
Čech complexes reveal valuable topological information about point sets at a certain scale in arbitrary dimensions, but the sheer size of these complexes limits their practical imp…