http://www.dagstuhl.de/17171

April 23 – 28 , 2017, Dagstuhl Seminar 17171

Computational Geometry

Organizers

Otfried Cheong (KAIST – Daejeon, KR)
Anne Driemel (TU Eindhoven, NL)
Jeff Erickson (University of Illinois – Urbana-Champaign, US)

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Documents

List of Participants
Shared Documents
Dagstuhl Seminar Schedule [pdf]

Motivation

Computational geometry is concerned with the design, analysis, and implementation of algorithms for geometric and topological problems, which arise naturally in a wide range of areas, including computer graphics, robotics, geographic information systems, molecular biology, sensor networks, machine learning, data mining, scientific computing, theoretical computer science, and pure mathematics. Computational geometry is a vibrant and mature field of research, with several dedicated international conferences and journals, significant real-world impact, and strong intellectual connections with other computing and mathematics disciplines.

Seminar Topics. The emphasis of the seminar will be on presenting recent developments in computational geometry, as well as identifying new challenges, opportunities, and connections to other fields of computing. In addition to the usual broad coverage of emerging results in the field, the seminar will include invited survey talks on two broad and overlapping focus areas that cover a wide range of both theoretical and practical issues in geometric computing. Both focus areas have seen exciting recent progress and offer numerous opportunities for further cross-disciplinary impact.

Computational geometry for monitoring and shape data. The combination of movement and geometry has always been an important topic in computational geometry, initially motivated by robotics and resulting in the study of kinetic data structures. With the advent of widely available location tracking technologies such as GPS sensors, trajectory analysis has become a topic in itself, which has connections to other classical topics in computational geometry such as shape analysis. Still, efficient technologies to perform the most basic operations are lacking. We need data structures supporting similarity queries on trajectory data and geometric clustering algorithms that can handle the infinite-dimensional geometry inherent in the data. A related type of data, namely time series data, has not received much attention in the computational geometry community, despite its universality and its close relation to trajectory data. Shedding light on the interconnections of these topics will promote new results in the field which will address these timely questions.

Computing in high-dimensional and infinite-dimensional spaces. The famous “curse of dimensionality” prevents exact geometric computations in high-dimensional spaces. Most of the data in science and engineering is high-dimensional, rendering classical geometric techniques, such as the sweepline approach, insufficient. One way to address this issue is to use sparsity, but it is not always easy to find a sparse representation of the data. The search of the most efficient representation and how to exploit this representation leads to dimension-reduction techniques, metric embeddings, and approximation algorithms. This line of research has strong ties to machine learning and discrete mathematics as well as computational geometry.

License
  Creative Commons BY 3.0 DE
  Otfried Cheong and Anne Driemel and Jeff Erickson

Dagstuhl Seminar Series

Classification

  • Data Structures / Algorithms / Complexity

Keywords

  • Combinatorics
  • Complexity
  • Algorithms
  • Geometric computing
  • Implementation
  • Applications
  • Monitoring and shape data
  • High-dimensional computational geometry

Book exhibition

Books from the participants of the current Seminar 

Book exhibition in the library, ground floor, during the seminar week.

Documentation

In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.

 

Download overview leaflet (PDF).

Publications

Furthermore, a comprehensive peer-reviewed collection of research papers can be published in the series Dagstuhl Follow-Ups.

Dagstuhl's Impact

Please inform us when a publication was published as a result from your seminar. These publications are listed in the category Dagstuhl's Impact and are presented on a special shelf on the ground floor of the library.

NSF young researcher support