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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, May 29, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jack Snoeyink (Univ. of North Carolina at Chapel Hill)

Convex hulls of intersections of line segments and planes

1. How much time does it take to compute the diameter or convex hull of the intersection points of a set of n lines (the finite vertices of their arrangement)?

2. What if you are given n line segments?

3. What if you are given n planes?

Over 20 years ago, Ching and Lee (and Atallah) answered the first question: Theta(n log n) time, even though the arrangement can have Theta(n^2) intersections -- the extreme points must be intersections of lines that are consecutive in slope order. This observation does not help us for questions #2 or #3, however. I'll present the answers in today's seminar.

This result has no known practical application, other than to partially refute Emo's accusation that I do applied work.

Joint work with Esther Arkin and Joseph Mitchell.

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