6 papers
Optimal Coresets for Hyperbolic Farthest-Point Queries via Ideal-Boundary Envelopes
Eunku Park
We study coresets for farthest-point queries in hyperbolic space. Given a nonempty finite set and , we seek a coreset $P_{\varepsilon}…
Quadratic Complexity of Voronoi Diagrams in for Lines in a Single Ruling of a Regulus
Eunku Park
We study nearest and farthest Voronoi diagrams of lines in under the Euclidean metric when all lines belong to one ruling of a smooth doubly ruled real quadric.…
Coresets for Continuous -Center in Hyperbolic Space
Eunku Park
We study the continuous -center problem in fixed-dimensional hyperbolic space. The input is a finite point set , while the centers may be placed anywhere…
Computing Topological Transition Sets for Line-Line-Circle Trisectors in
Eunku Park
Computing the Voronoi diagram of mixed geometric objects in is challenging due to the high cost of exact geometric predicates via Cylindrical Algebraic Decomposition (CAD). W…
Coresets for Farthest Point Problems in Hyperbolic Space
Eunku Park, Antoine Vigneron
We show how to construct in linear time coresets of constant size for farthest point problems in fixed-dimensional hyperbolic space. Our coresets provide both an arbitrarily small…
Embeddings and near-neighbor searching with constant additive error for hyperbolic spaces
Eunku Park, Antoine Vigneron
We give an embedding of the Poincaré halfspace into a discrete metric space based on a binary tiling of , with additive distortion . It yields the following r…