Algorithmic Geometry

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.