Author
Herbert Edelsbrunner
Other affiliations: University of Illinois at Urbana–Champaign, Duke University, Graz University of Technology ...read more
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 published on a yearly basis
Papers
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20 Apr 1998TL;DR: A unified view of algorithmic solutions proposed in the computer science literature that are based on the Delaunay complex of the points is presented.
Abstract: The reconstruction of a shape or surface from a finite set of points is a practically significant and theoretically challenging problem. This paper presents a unified view of algorithmic solutions proposed in the computer science literature that are based on the Delaunay complex of the points.
109 citations
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TL;DR: A variety of problems on the interaction between two sets of line segments in two and three dimensions are considered, including counting the number of intersecting pairs between m blue segments andn red segments in the plane.
Abstract: We consider a variety of problems on the interaction between two sets of line segments in two and three dimensions. These problems range from counting the number of intersecting pairs between m blue segments andn red segments in the plane (assuming that two line segments are disjoint if they have the same color) to finding the smallest vertical distance between two nonintersecting polyhedral terrains in three-dimensional space. We solve these problems efficiently by using a variant of the segment tree. For the three-dimensional problems we also apply a variety of recent combinatorial and algorithmic techniques involving arrangements of lines in three-dimensional space, as developed in a companion paper.
109 citations
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01 Jan 2003TL;DR: In this article, the authors describe an unambiguous definition of a surface in geometric and topological terms, and sketch a fast algorithm for constructing it, which overcomes past limitations to special point distributions and heuristic design decisions.
Abstract: Given a finite point set in ℝ3, the surface reconstruction problem asks for a surface that passes through many but not necessarily all points. We describe an unambiguous definition of such a surface in geometric and topological terms,and sketch a fast algorithm for constructing it. Our solution overcomes past limitations to special point distributions and heuristic design decisions.
109 citations
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TL;DR: In this paper, the authors introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution and present the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations.
Abstract: We introduce a multiscale topological description of the Megaparsec web-like cosmic matter distribution. Betti numbers and topological persistence offer a powerful means of describing the rich connectivity structure of the cosmic web and of its multiscale arrangement of matter and galaxies. Emanating from algebraic topology and Morse theory, Betti numbers and persistence diagrams represent an extension and deepening of the cosmologically familiar topological genus measure and the related geometric Minkowski functionals. In addition to a description of the mathematical background, this study presents the computational procedure for computing Betti numbers and persistence diagrams for density field filtrations. The field may be computed starting from a discrete spatial distribution of galaxies or simulation particles. The main emphasis of this study concerns an extensive and systematic exploration of the imprint of different web-like morphologies and different levels of multiscale clustering in the corresponding computed Betti numbers and persistence diagrams. To this end, we use Voronoi clustering models as templates for a rich variety of web-like configurations and the fractal-like Soneira-Peebles models exemplify a range of multiscale configurations. We have identified the clear imprint of cluster nodes, filaments, walls, and voids in persistence diagrams, along with that of the nested hierarchy of structures in multiscale point distributions. We conclude by outlining the potential of persistent topology for understanding the connectivity structure of the cosmic web, in large simulations of cosmic structure formation and in the challenging context of the observed galaxy distribution in large galaxy surveys.
108 citations
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TL;DR: The proof takes an algorithmic approach, that is, an algorithm is described for the calculation of thesem faces and the upper bound for the total number of edges is derived from the analysis of the algorithm.
Abstract: We show that the total number of edges ofm faces of an arrangement ofn lines in the plane isO(m2/3??n2/3+2?+n) for any?>0. The proof takes an algorithmic approach, that is, we describe an algorithm for the calculation of thesem faces and derive the upper bound from the analysis of the algorithm. The algorithm uses randomization and its expected time complexity isO(m2/3??n2/3+2? logn+n logn logm). If instead of lines we have an arrangement ofn line segments, then the maximum number of edges ofm faces isO(m2/3??n2/3+2?+n? (n) logm) for any?>0, where?(n) is the functional inverse of Ackermann's function. We give a (randomized) algorithm that produces these faces and takes expected timeO(m2/3??n2/3+2? log+n?(n) log2n logm).
108 citations
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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
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08 Sep 2000TL;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
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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
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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