17 citations · 23 across the 5 of their papers we have counts for
6 papers
A Pseudoline Counterexample to the Strong Dirac Conjecture
Ben D. Lund, George B. Purdy, Justin W. Smith
We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. This shows t…
Collinearities in Kinetic Point Sets
Ben D. Lund, George B. Purdy, Justin W. Smith +1
Let be a set of points in the plane, each point moving along a given trajectory. A {\em -collinearity} is a pair of a line and a time such that conta…
A Bichromatic Incidence Bound and an Application
Ben D. Lund, George B. Purdy, Justin W. Smith
We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}…
A Multi-Stage CUDA Kernel for Floyd-Warshall
Ben Lund, Justin W Smith
We present a new implementation of the Floyd-Warshall All-Pairs Shortest Paths algorithm on CUDA. Our algorithm runs approximately 5 times faster than the previously best reported…
On Finding Ordinary or Monochromatic Intersection Points
George B. Purdy, Justin W. Smith
An algorithm is demonstrated that finds an ordinary intersection in an arrangement of lines in , not all parallel and not all passing through a common point, in t…
Lines, Circles, Planes and Spheres
George B. Purdy, Justin W. Smith
Let be a set of points in , no three collinear and not all coplanar. If at most are coplanar and is sufficiently large, the total number of planes d…