Showing papers on "Convex hull algorithms published in 2001"

Determining the Convex Hull in Large Multidimensional Databases

Abstract: Determining the convex hull of a point set is a basic operation for many applications of pattern recognition, image processing, statistics, and data mining. Although the corresponding point sets are often large, the convex hull operation has not been considered much in a database context, and state-of-the-art algorithms do not scale well to non main-memory resident data sets. In this paper, we propose two convex hull algorithms which are based on multidimensional index structures such as R-trees. One of them traverses the index depth-first. The other algorithm assigns a priority to each active node (nodes which are not yet accessed but known to the system), which corresponds to the maximum distance of the node region to the tentative convex hull. We show both theoretically as well as experimentally that our algorithms outperform competitive techniques that do not exploit indexes.

Formalizing convex hull algorithms

Abstract: We study the development of formally proved algorithms for computational geometry The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs A special attention has been given to handling degenerate cases that are often overlooked by conventional algorithm presentations

Formalizing Convex Hull Algorithms

Abstract: We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs. A special attention has been given to handling degenerate cases that are often overlooked by conventional algorithm presentations.