On the Combinatorial and Topological Complexity of a Single Cell

Résumé du livre

Abstract: "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 R[superscript k] 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(n[superscript k-1] rather than O(n[superscript k]) which is the bound for the combinatorial complexity of the whole arrangement. Currently, this is known to be true only for k [