Preprocessing 2D data for fast convex hull computations

Tropical Convex Hull Computations

This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial ideals, subdivisions of products of simplices, matroid theory, finite metric spaces, and the tropical Grassmannians. The relationship between these topics is expl...

Convex Hull Computations

The “convex hull problem” is a catch-all phrase for computing various descriptions of a polytope that is either specified as the convex hull of a finite point set in R or as the intersection of a finite number of halfspaces. We first define the various problems and discuss their mutual relationships (Section 26.1). We discuss the very special case of the irredundancy problem in Section 26.2. We...

A Straightforward Preprocessing Approach for Accelerating Convex Hull Computations on the GPU

An effective strategy for accelerating the calculation of convex hulls for point sets is to filter the input points by discarding interior points. In this paper, we present such a straightforward and efficient preprocessing approach by exploiting the GPU. The basic idea behind our approach is to discard the points that locate inside a convex polygon formed by 16 extreme points. Due to the fact ...

Fast approximation of convex hull

The construction of a planar convex hull is an essential operation in computational geometry. It has been proven that the time complexity of an exact solution is Ω(NlogN). In this paper, we describe an algorithm with time complexity O(N + k), where k is parameter controlling the approximation quality. This is beneficial for applications processing a large number of points without necessity of a...

Measuring Interval Efficiency in Convex Hull of Data Using DEA