The Combinatorial and Topological Complexity of a Single Cell

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作者：
机构：
[1] School of Mathematics and College of Computing,
[2] Georgia Institute of Technology,undefined
[3] Atlanta,undefined
[4] GA 30332,undefined
[5] USA saugata@math.gatech.edu,undefined
来源：
Discrete & Computational Geometry | 2002年 / 29卷
关键词：
Single Cell; High Dimension; Algebraic Geometry; Classic Result; Computational Geometry;
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摘要：
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 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 complexity of the whole arrangement. Until now, this was known to be true only for k ≤ 3 and only for some special cases in higher dimensions.
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页码：41 / 59
页数：18
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