## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, April 20, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Michael Hoffmann (2) (University of Leicester)

## Efficient Update Strategies for Geometric Computing with Uncertainty

We consider the problems of computing maximal points and the convex hull of a set of points in 2D, when the points are in motion.'' We assume that the point locations (or trajectories) are not known precisely and determining these values exactly is feasible, but expensive. In our model, the algorithm only knows areas within which each of the input points lie, and is required to identify the maximal points or points on the convex hull correctly by updating some points (i.e. determining exactly their location). We compare the number of points updated by the algorithm on a given instance to the minimum number of points that must be updated by a nondeterministic strategy in order to provably compute the answer correctly. We give algorithms for both of the above problems that always update at most 3 times as many points as the nondeterministic strategy, and show that this is the best possible.

(Joint work with Rajeev Raman and Danny Krizanc)

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