Andrea Francke
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Andrea Francke has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Heidi Gebauer
Institute of Theoretical Computer Science, ETH Zurich, CH-8092, Switzerland
1 shared publication - Jiří Matoušek
Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
1 shared publication - Takeaki Uno
National Institute of Informatics, Tokyo, Japan
1 shared publication - Tobias Christ
Institute of Theoretical Computer Science ETH Zurich 8092 Zurich Switzerland
1 shared publication
Latest Publications
- Open Access
A Doubly Exponentially Crumbled Cake
We consider the following cake cutting game: Alice chooses a set P of n points in the square (cake) [0,1]^2, where (0,0) is in P; Bob cuts out n axis-parallel rectangles with disjoint interiors, each of them having a point of P as the lower left corner; Alice keeps the rest. It has been conjectured that Bob can always secure at least half of the cake. This remains unsettled, and it is not even known whether Bob can get any positive fraction independent of n. We prove that if Alice can force Bob's share to tend to zero, then she must use very many points; namely, to prevent Bob from gaining more than 1/r of the cake, she needs at least 2^{2^{\Omega(r)}} points.
Open AccessA Doubly Exponentially Crumbled Cake
We consider the following cake cutting game: Alice chooses a set P of n points in the square (cake) [0,1]^2, where (0,0) is in P; Bob cuts out n axis-parallel rectangles with disjoint interiors, each of them having a point of P as the lower left corner; Alice keeps the rest. It has been conjectured that Bob can always secure at least half of the cake. This remains unsettled, and it is not even known whether Bob can get any positive fraction independent of n. We prove that if Alice can force Bob's share to tend to zero, then she must use very many points; namely, to prevent Bob from gaining more than 1/r of the cake, she needs at least 2^{2^{\Omega(r)}} points.