A triangulation of a planar point set S is a maximal plane straight-line graph with vertex set S. In the minimum weight triangulation (MWT) problem, we are looking for a triangulation of a givenâ€¦ (More)

Given a planar graph G, the graph theoretic dilation of G is defined as the maximum ratio of the shortest-path distance and the Euclidean distance between any two vertices of G. Given a planar pointâ€¦ (More)

Let P be a d-dimensional n-point set. A Tverberg partition of P is a partition of P into r sets P1, ..., Pr such that the convex hulls ch(P1), ..., ch(Pr) have non-empty intersection. A point in theâ€¦ (More)

We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an arbitrary, unknown input distribution. We give suchâ€¦ (More)

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 constant-work-space algorithm has read-only access to an input array and may use only O(1) additional words of O(log n) bits, where n is the input size. We show how to triangulate a planeâ€¦ (More)

Over the last decade, there have been several data structures that, given a planar subdivision and a probability distribution over the plane, provide a way for answering point location queries thatâ€¦ (More)

Given a planar graph G, the graph theoretic dilation of G is defined as the maximum ratio of the shortestpath distance and the Euclidean distance between any two vertices of G. Given a planar pointâ€¦ (More)

In the limited-workspace model, we assume that the input of size n lies in a random access read-only memory. The output has to be reported sequentially, and it cannot be accessed or modified. Inâ€¦ (More)