Most of my work is in the field of computational geometry, where I explore how additional structure in the inputs can be exploited to find faster algorithms for classical problems, like Delaunayâ€¦ (More)

A set P = H âˆª {w} of n + 1 points in the plane is called a wheel set if all points but w are extreme. We show that for the purpose of counting crossing-free geometric graphs on P , it suffices toâ€¦ (More)

We show that every triangulation (maximal planar graph) on n â‰¥ 6 vertices can be flipped into a Hamiltonian triangulation using a sequence of less than n/2 combinatorial edge flips. The previouslyâ€¦ (More)

We describe a framework for counting and enumerating various types of crossing-free geometric graphs on a planar point set. The framework generalizes ideas of Alvarez and Seidel, who used them toâ€¦ (More)

The d-dimensional Catalan numbers form a well-known sequence of numbers which count balanced bracket expressions over an alphabet of size d. In this paper, we introduce and study what we callâ€¦ (More)