Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, October 23, 2007, 12:15 pm

**Duration**: This information is not available in the database

**Location**: OAT S15/S16/S17

**Speaker**: Marek Sulovský

I will present one or two discrete geometric results dealing with curves in the plane. First of them is a recent upper bound O(n^(2-1/2s)) [Chan '05] on the complexity of k-levels in an arrangement of s-intersecting curve segments in the plane (where k-level is a closure of the set of all points lying on some of the curve segments, which have exactly k curve segments below them). Although the proof of this result is very simple, a better than quadratic bound has not been known for a long time.

If time permits, I will also talk about the upper bound on the complexity of k-level in an arrangement of lines, which is O(n^(4/3)) [Dey '98] and try to explain, how a theorem about singularities of curves can be used to prove this upper bound.

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