https://www.dagstuhl.de/9041

### October 8 – 12 , 1990, Dagstuhl Seminar 9041

# Algorithmic Geometry

## Organizer

H. Alt, E. Welzl

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## Documents

## Summary

The first Dagstuhl-seminar on Computational Geometry was organized by Helmut Alt and Emo Welzl (both FU Berlin). The 28 participants came from 10 countries, 7 of them came from North America and Israel.

20 lectures were given at the seminar, covering quite a number of topics in computational geometry. As was to be expected, a large percentage of the talks dealt with randomization in one way or the other, reflecting the current inclination of the community towards this field. Accordingly, a special discussion session on randomized algorithms was held, which in fact attracted most of the participants of the seminar.

Furthermore, two lectures dealt with the actual implementation of geometric algorithms, and two library / development systems were presented.

Other lectures dealt with problems concerning the similarity of two objects, e.g. matching points into regions, or measuring the (Hausdorff-) distance between polygons.

However, the most unforgettable event of the seminar was clearly the open problem
session on monday evening, chaired by Ricky Pollack. It was there that Raimund
Seidel declared the zone theorem an open problem, since the proof by Edelsbrunner,
O'Rourke, Seidel (given e.g. in the book by Herbert Edelsbrunner) is incorrect. The
excitement was considerable, and still rose when Jirka Matousek pulled out of his bag
a short manuscript entitled A *simple proof of weak zone theorem*! Micha Sharir also
presented some ideas as to how to prove a weak zone theorem, and now there seems
to be a new proof for the zone theorem by Herbert Edelsbrunner which proceeds
along the same lines.

## Dagstuhl Seminar Series

- 23221: "Computational Geometry" (2023)
- 21181: "Computational Geometry" (2021)
- 19181: "Computational Geometry" (2019)
- 17171: "Computational Geometry" (2017)
- 15111: "Computational Geometry" (2015)
- 13101: "Computational Geometry" (2013)
- 11111: "Computational Geometry" (2011)
- 09111: "Computational Geometry" (2009)
- 07111: "Computational Geometry" (2007)
- 05111: "Computational Geometry" (2005)
- 03121: "Computational Geometry" (2003)
- 01121: "Computational Geometry" (2001)
- 99102: "Computational Geometry" (1999)
- 9707: "Computational Geometry" (1997)
- 9511: "Computational Geometry" (1995)
- 9312: "Computational Geometry" (1993)
- 9141: "Computational Geometry" (1991)