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: Thursday, July 12, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Vissarion Fisikopoulos (National and Kapodistrian University of Athens)

Constructing Polytopes via a Vertex Oracle

We develop a new paradigm to construct polytopes whose vertices can be obtained by an effective oracle in a unique fashion. Starting with the Newton polytope of the resultant, our method also efficiently computes secondary polytopes as well as the Newton polytope of the discriminant. We propose an output-sensitive algorithm that requires the minimum number of oracles, each reducing to the construction of a regular triangulation of the input pointset. The C++ implementation of this algorithm has allowed us to compute resultant polytopes in 7 or 8 dimensions. It has also yielded the most complex 3d and 4d resultant polytopes, the latter with f-vector (22,66,66,22,1), thus opening the study of this polytope family. Finally, we discuss open algorithmic problems regarding such polytopes.

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