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 M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, April 25, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Manuel Wettstein

An Optimal Algorithm for Reconstructing Point Set Order Types from Radial Orderings

Let P be a set of n points in the plane. The order type \chi of P is a function which assigns an orientation (clockwise or counterclockwise) to every ordered triple in P. The radial system R of P describes the (counterclockwise) radial order in which all other points are encountered around each point in P. While given \chi it is easy to construct the corresponding R, the converse is not true and there might be more than one solution. We give an algorithm that takes R as input and, after O(n) time of preprocessing, allows constant-time queries to all order types that are consistent with R.
Joint work with Oswin Aichholzer, Vincent Kusters, Wolfgang Mulzer, and Alexander Pilz.

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