Publications with Christian Knauer
- Covering many points with a small-area box.
M. De Berg, S. Cabello, O. Cheong, D. Eppstein, and C. Knauer.
arXiv:1612.02149.
J. Computational Geometry 10 (1): 207–222, 2019.
We give an efficient algorithm for finding the smallest axis-parallel rectangle covering a given number of points out of a larger set of points in the plane.
- Better late than never: the complexity of arrangements of polyhedra.
B. Aronov, S. W. Bae, O. Cheong, D. Eppstein, C. Knauer, and R. Seidel.
41st European Workshop on Computational Geometry (EuroCG 2025), Liblice, Czech Republic, pp. 62:1–62:4.
arXiv:2506.03960.
My 1994 paper "On the number of minimal 1-Steiner trees" with Aronov and Bern, in some preliminary manuscript versions, included a bound of \(O(m^{\lceil d/2\rceil}n^{\lfloor d/2\rfloor})\) on the complexity of an arrangement of \(m\) convex polytopes given as intersections of a total of \(n\) halfspaces, interpolating between the upper bound theorem for polytopes and the complexity of hyperplane arrangements. However, the manuscript and the proof were lost. This paper re-proves the result, with better care for the degenerate cases.