Generalized Convex Hull Combination Approach

Generalized Convex Disjunctive Programming: Nonlinear Convex Hull Relaxation

Kinetic Convex Hull; an Analytical Approach

In this paper, first, we present a kinetic data structure for the problem of kinetic convex hull maintenance. After that, discuss some complicated cases followed by the main algorithm and two additional algorithms. Finally, focus on the evaluation of the four properties of the kinetic algorithm in the worst case. We show that quality factors of our algorithm are at most linear. Comparing with s...

On Generalized Planar Skyline and Convex Hull Range Queries

We present output sensitive techniques for the generalized reporting versions of the planar range maxima problem and the planar range convex hull problem. Our solutions are in the pointer machine model, for orthogonal range queries on a static point set. We solve the planar range maxima problem for two-sided, three-sided and four-sided queries. We achieve a query time of O(log n+c) using O(n) s...

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...