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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.


Papers
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Journal ArticleDOI
TL;DR: It is shown that, given a set S of n points in R3, one can always find three planes that form an eight-partition of S, that is, a partition where at most n/8 points of S lie in each of the eight open regions.
Abstract: It is shown that, given a set S of n points in R3, one can always find three planes that form an eight-partition of S, that is, a partition where at most n/8 points of S lie in each of the eight open regions. This theorem is used to define a data structure, called an octant tree, for representing any point set in R3. An octant tree for n points occupies O(n) space and can be constructed in polynomial time. With this data structure and its refinements, efficient solutions to various range query problems in 2 and 3 dimensions can be obtained, including (1) half-space queries: find all points of S that lie to one side of any given plane; (2) polyhedron queries: find all points that lie inside (outside) any given polyhedron; and (3) circular queries in R2: for a planar set S, find all points that lie inside (outside) any given circle. The retrieval time for all these queries is T(n)=O(na + m) where a= 0.8988 (or 0.8471 in case (3)) and m is the size of the output. This performance is the best currently known for linear-space data structures which can be deterministically constructed in polynomial time.

43 citations

Journal ArticleDOI
TL;DR: A method is given that constructs a skeleton inO(√n logn) time per edge that implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams in E2 and space cutting trees in E3.
Abstract: An edge-skeleton in an arrangementA(H) of a finite set of planes inE3 is a connected collection of edges inA(H). We give a method that constructs a skeleton inO(√n logn) time per edge. This method implies new and more efficient algorithms for a number of structures in computational geometry including order-k power diagrams inE2 and space cutting trees inE3.

42 citations

Journal ArticleDOI
TL;DR: An algorithm is described that constructs homeomorphisms with prescribed area distortion that can be used to generate cartograms, which are geographic maps purposely distorted so their area distributions reflects a variable different from area, as for example population density.
Abstract: A homeomorphism from R 2 to itself distorts metric quantities, such as distance and area. We describe an algorithm that constructs homeomorphisms with prescribed area distortion. Such homeomorphisms can be used to generate cartograms, which are geographic maps purposely distorted so their area distributions reflects a variable different from area, as for example population density. The algorithm generates the homeomorphism through a sequence of local piecewise linear homeomorphic changes. Sample results produced by the preliminary implementation of the method are included.

42 citations

Proceedings ArticleDOI
06 Jan 1988
TL;DR: A (randomized) algorithm is given that produces these faces and, with high probability, takes time that is within a log 2-supscrpt factor of the combinatorial bound.
Abstract: We show that the total number of edges of m faces of an arrangement of n lines in the plane is O(m2/3-dn2/3+2d + n), for any d > 0. The proof takes an algorithmic approach, that is, we describe an algorithm for the calculation of these m faces and derive the upper bound from the analysis of the algorithm. The algorithm uses randomization and, with high probability, its time complexity is within a log2n factor of the above bound. If instead of lines we have an arrangement of n line segments, then the maximum number of edges of m faces is Ogr;(m2/3-dn2/3+2d + na(n)logm), for any d > 0, where a(n) is the functional inverse of Ackermann's function. We give a (randomized) algorithm that produces these faces and, with high probability, takes time that is within a log2n factor of the combinatorial bound.

42 citations


Cited by
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Journal ArticleDOI
TL;DR: The goals of the PDB are described, the systems in place for data deposition and access, how to obtain further information and plans for the future development of the resource are described.
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.

34,239 citations

Book
08 Sep 2000
TL;DR: This book presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects, and provides a comprehensive, practical look at the concepts and techniques you need to get the most out of real business data.
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

23,600 citations

Book
25 Oct 1999
TL;DR: 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.
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

20,196 citations

MonographDOI
01 Jan 2006
TL;DR: This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms, into planning under differential constraints that arise when automating the motions of virtually any mechanical system.
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.

6,340 citations