Herbert Edelsbrunner

Bio: Herbert Edelsbrunner is an academic researcher from Institute of Science and Technology Austria. The author has contributed to research in topics: Delaunay triangulation & Voronoi diagram. The author has an hindex of 84, co-authored 377 publications receiving 33877 citations. Previous affiliations of Herbert Edelsbrunner include University of Illinois at Urbana–Champaign & Duke University.

Testing the necklace condition for shortest tours and optimal factors in the plane

Abstract: A tour τ of a finite set P of points is a necklace-tour if there are disks with the points in P as centers such that two disks intersect if and only if their centers are adjacent in τ. It has been observed by Sanders that a necklace-tour is an optimal traveling salesman tour.

Multiple covers with balls I: Inclusion–exclusion

Abstract: Inclusion–exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion–exclusion formulas for the subset of R n covered by at least k balls in a finite set. We implement two of the formulas in dimension n = 3 and report on results obtained with our software.

On the optimality of functionals over triangulations of Delaunay sets

Abstract: In this short paper we consider the functional density on sets of uniformly bounded triangulations with fixed sets of vertices. We prove that if a functional attains its minimum on the Delaunay triangulation for every finite set in the plane, then for infinite sets the density of this functional attains its minimum also on the Delaunay triangulations. A Delaunay set in E is a set of points X for which there are positive numbers r and R such that every open d-ball of radius r contains at most one point and every closed d-ball of radius R contains at least one point of X. In this paper we consider Delaunay sets in general position, that is, no d + 2 points in X lie on a common (d− 1)-sphere. By a triangulation of X we mean a simplicial complex whose vertex set is X. For finite sets the simplices decompose the convex hull of the set, while for Delaunay sets X the simplices decompose E. We say that a triangulation T is uniformly bounded if there exists a positive number q = q(T ) that is greater than or equal to the circumradii of all d-simplices in the triangulation: R(S) 6 q for all d-simplices S of T . We denote the family of all uniformly bounded triangulations of X by Θ(X). Delaunay sets were introduced byBorisDelaunay (1924), who called them (r, R)-systems. He proved that for any Delaunay set X there exists a unique Delaunay tesselation DT (X) (see, for instance, [1]). If X is in general position, then DT (X) is a triangulation of X in the sense defined above. Since the circumradius of any simplex is at most R, the Delaunay triangulation is uniformly bounded with q = R, that is, DT (X) ∈ Θ(X). We note that every Delaunay set also has triangulations that are not uniformly bounded, and it is not difficult to construct them. We want to remind the reader of a related open problem about Delaunay sets: is it true that for every planar Delaunay set X and every positive number C there exists a triangle ∆ that contains none of the points in X and has area greater than C? While we heard of this question from Michael Boshernitzan, it is sometimes referred to as Danzer’s problem. Let F be a functional defined on d-simplices S. (For instance, F (S) may be the sum of squares of edge lengths multiplied by the volume of S.) We only consider functionals that are continuous with respect to the parameters describing the simplices, for example, the lengths of their edges. Let X be a finite set in E and T any triangulation of X. Then F can be defined on T as F (T ) = ∑ S∈T F (S). It is clear that this definition cannot be used for infinite sets. We therefore define the (lower) density of F for a uniformly bounded triangulation T of a Delaunay set X as

Analysis of Dynamic Message Passing Programs (A framework for the analysis of depth-bounded systems )

Abstract: Motivated by the analysis of highly dynamic message-passing systems, i.e. unbounded thread creation, mobility, etc. We present a framework for the analysis of depth-bounded systems. Depth-bounded systems are one of the most expressive known fragment of the π-calculus for which interesting verification problems are still decidable. Even though they are infinite state systems depth-bounded systems are well-structured, thus can be analyzed algorithmically. We give an interpretation of depth-bounded systems as graph-rewriting systems. This gives more flexibility and ease of use to apply depth-bounded systems to other type of systems like shared memory concurrency. First, we develop an adequate domain of limits for depth-bounded systems, a prerequisite for the effective representation of downward-closed sets. Downwardclosed sets are needed by forward saturation-based algorithms to represent potentially infinite sets of states. Then, we present an abstract interpretation framework to compute the covering set of well-structured transition systems Because, in general, the covering set is not computable, our abstraction overapproximates the actual covering set. Our abstraction captures the essence of acceleration based-algorithms while giving up enough precision to ensure convergence. We have implemented the analysis in the Picasso tool and show that it is accurate in practice. Finally, we build some further analyses like termination using the covering set as starting point.

The Protein Data Bank

Abstract: The Protein Data Bank (PDB; http://www.rcsb.org/pdb/ ) is the single worldwide archive of structural data of biological macromolecules. This paper describes the goals of the PDB, the systems in place for data deposition and access, how to obtain further information, and near-term plans for the future development of the resource.

Data Mining: Concepts and Techniques

Abstract: The increasing volume of data in modern business and science calls for more complex and sophisticated tools. Although advances in data mining technology have made extensive data collection much easier, it's still always evolving and there is a constant need for new techniques and tools that can help us transform this data into useful information and knowledge. Since the previous edition's publication, great advances have been made in the field of data mining. Not only does the third of edition of Data Mining: Concepts and Techniques continue the tradition of equipping you with an understanding and application of the theory and practice of discovering patterns hidden in large data sets, it also focuses on new, important topics in the field: data warehouses and data cube technology, mining stream, mining social networks, and mining spatial, multimedia and other complex data. Each chapter is a stand-alone guide to a critical topic, presenting proven algorithms and sound implementations ready to be used directly or with strategic modification against live data. This is the resource you need if you want to apply today's most powerful data mining techniques to meet real business challenges. * Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects. * Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields. *Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data

Data Mining: Practical Machine Learning Tools and Techniques

Abstract: Data Mining: Practical Machine Learning Tools and Techniques offers a thorough grounding in machine learning concepts as well as practical advice on applying machine learning tools and techniques in real-world data mining situations. This highly anticipated third edition of the most acclaimed work on data mining and machine learning will teach you everything you need to know about preparing inputs, interpreting outputs, evaluating results, and the algorithmic methods at the heart of successful data mining. Thorough updates reflect the technical changes and modernizations that have taken place in the field since the last edition, including new material on Data Transformations, Ensemble Learning, Massive Data Sets, Multi-instance Learning, plus a new version of the popular Weka machine learning software developed by the authors. Witten, Frank, and Hall include both tried-and-true techniques of today as well as methods at the leading edge of contemporary research. *Provides a thorough grounding in machine learning concepts as well as practical advice on applying the tools and techniques to your data mining projects *Offers concrete tips and techniques for performance improvement that work by transforming the input or output in machine learning methods *Includes downloadable Weka software toolkit, a collection of machine learning algorithms for data mining tasks-in an updated, interactive interface. Algorithms in toolkit cover: data pre-processing, classification, regression, clustering, association rules, visualization

Planning Algorithms: Introductory Material

Abstract: Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.