23. – 28. April 2017, Dagstuhl-Seminar 17171

Computational Geometry


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

Auskunft zu diesem Dagstuhl-Seminar erteilt

Dagstuhl Service Team


Dagstuhl Report, Volume 7, Issue 4 Dagstuhl Report
Programm des Dagstuhl-Seminars [pdf]


Computational Gemoetry

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, CAD, robotics, computer vision, image processing, spatial databases, GIS, 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 and strong intellectual connections with other computing and mathematics disciplines.

Seminar Topics

The emphasis of the seminar was 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 new results in the field, the seminar included broad survey talks on monitoring and shape data and on high-dimensional geometric computing, two focus areas that have seen exciting recent progress and that present 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.


Dagstuhl seminars on computational geometry have been organized in a two year rhythm since a start in 1990. They have been extremely successful both in disseminating the knowledge and identifying new research thrusts. Many major results in computational geometry were first presented in Dagstuhl seminars, and interactions among the participants at these seminars have led to numerous new results in the field. These seminars have also played an important role in bringing researchers together, fostering collaboration, and exposing young talent to the seniors of the field. They have arguably been the most influential meetings in the field of computational geometry. The organizers held a lottery for the third time this year; the lottery allows to create space to invite younger researchers, rejuvenating the seminar, while keeping a large group of senior and well-known scholars involved. The seminar has now a more balanced attendance in terms of seniority and gender than in the past. This year, 47 researchers from various countries and continents attended the seminar, showing the strong interest of the community for this event. The feedback from participants was very positive. No other meeting in our field allows young researchers to meet with, get to know, and work with well-known and senior scholars to the extent possible at the Dagstuhl Seminar. We warmly thank the scientific, administrative and technical staff at Schloss Dagstuhl! Dagstuhl allows people to really meet and socialize, providing them with a wonderful atmosphere of a unique closed and pleasant environment, which is highly beneficial to interactions. Therefore, Schloss Dagstuhl itself is a great strength of the seminar.

Summary text license
  Creative Commons BY 3.0 Unported license
  Otfried Cheong, Anne Driemel, and Jeff Erickson

Dagstuhl-Seminar Series


  • Data Structures / Algorithms / Complexity


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


In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.


Download Übersichtsflyer (PDF).

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