A Reliable Convex-Hull Algorithm for Interval-Based Hierarchical Structures

Abstract

This paper presents a new approach for constructing the convex polyhedral enclosure of an interval-based hierarchical structure of any dimension. To reduce the number of points in the hull construction considered, only relevant vertices on the boundary-called presumable extreme points- are involved. Additionally, a suitable update of the presumable extreme points enhances the performance whenever the maximum level of the hierarchical structure is changed. This method utilizes interval arithmetic and combines adaptation of the concept of presumable extreme points to higher dimensions with a convex-hull algorithm based on an interval linear solver.