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Dagstuhl Seminar 23221

Computational Geometry

( May 29 – Jun 02, 2023 )

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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.

The emphasis of the seminar is 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 Dagstuhl Seminar will include broad survey talks with a special focus on two areas. First, processing and application of uncertain and probabilistic geometric data. Second, is reconfiguration. Both topics have seen deep recent technical development and connections with geometric application domains such as data management, robotics, and graph drawing.

Processing and Applications of Uncertain and Probabilistic Geometric Data
As uncertain and probabilistic data is produced in increasing volume by sensing devices, the processing and applications of such data is becoming an emerging theme. Several basic problems in computational geometry such as convex hull and minimum spanning tree have been reexamined in this new setting. The processing of uncertain or probabilistic data in privacy, geometric optimization, nearest neighbor search, and range searching have also opened up new research directions. The topic of uncertain and probabilistic geometric data will also connect computational geometry to other disciplines, such as database and machine learning, in which there are also more research works with similar themes.

Reconfiguration problems have been long studied in combinatorial mathematics. There is a long history of research on the structure of reconfiguration graphs of discrete geometric and topological objects, such as for instance flip graphs of triangulations or rectangular subdivisions, Reidemeister graphs in knot theory, etc. Indeed, many researchers in computational geometry who are also active in adjacent fields such as graph theory and combinatorial topology have long investigated such reconfiguration problems.

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 hold a lottery to create space to invite less senior researchers, while keeping a large group of senior and well-known scholars involved.

Copyright Siu-Wing Cheng, Maarten Löffler, and Jeff M. Phillips

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  • Computational Geometry
  • Data Structures and Algorithms
  • Discrete Mathematics

  • combinatorics
  • algorithms
  • geometric computing
  • uncertainty
  • reconfiguration