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

Date and Time: Tuesday, December 21, 2021, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nicolas Grelier

Improved approximation algorithm for the Minimum Convex Partition problem

Given a set of points P, the minimum convex partition problem consists in partitioning the convex hull of P into convex polygons, such that no convex polygon contains a point in P in its interior, and the interiors of the convex polygons are pairwise disjoint. We consider the two variants whether we constrain the vertices of the polygons to be in P. In a previous talk, we showed that this problem is NP-hard, and that there exists an O(sqrt(n)log(n))-approximation algorithm. In this talk, we show the existence of an O(log(OPT))-approximation algorithm, where OPT denotes the minimum number of convex faces required.

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