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

Date and Time: Tuesday, November 12, 2013, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Alexander Pilz (TU Graz)

Combinatorial Algorithms for Combinatorial Problems: Selection of Extreme Points

We consider problems on finite point sets in the Euclidean plane. The concept of point set order types allows us to group the infinite number of different point sets of a given size into a finite collection of order types by the way each triple is oriented.

While for many problems in Computational Geometry the solution is the same for all point sets that have the same order type, many algorithms use the additional geometric information encoded in the point coordinates. Our main goal is to remove these dependencies and still obtain runtime-optimal algorithms.

In this talk, we give a short introduction to the concept of order types and their abstraction. We state several motivations for devising purely combinatorial algorithms for suitable geometric problems. Finally, we give examples of algorithms that work with information from the reduced setting only, in particular discussing the selection of an edge of the convex hull of a point set intersecting a given ray in linear time.

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