The Combinatorial and Topological Complexity of a Single Cell

@article{Basu2003TheCA,
  title={The Combinatorial and Topological Complexity of a Single Cell},
  author={Saugata Basu},
  journal={Discrete & Computational Geometry},
  year={2003},
  volume={29},
  pages={41-59}
}
The problem of bounding the combinatorial complexity of a single connected component (a single cell) of the complement of a set of n geometric objects in Rk, each object of constant description complexity, is an important problem in computational geometry which has attracted much attention over the past decade. It has been conjectured that the combinatorial complexity of a single cell is bounded by a function much closer to O(nk−1) rather than O(nk) which is the bound for the combinatorial… CONTINUE READING