论文信息 - Vertical decomposition of arrangements of hyperplanes in four dimensions

Vertical decomposition of arrangements of hyperplanes in four dimensions

We show that, for any collection ℋ ofn hyperplanes in ℜ4, the combinatorial complexity of thevertical decomposition of the arrangementA(ℋ) of ℋ isO(n4 logn). The proof relies on properties of superimposed convex subdivisions of 3-space, and we also derive some other results concerning them.

Leonidas J. Guibas | Micha Sharir | Jirí Matousek | Dan Halperin

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