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COMPGEOM
2009
ACM

Computing hereditary convex structures

13 years 10 months ago
Computing hereditary convex structures
Color red and blue the n vertices of a convex polytope P in R3 . Can we compute the convex hull of each color class in o(n log n)? What if we have χ > 2 colors? What if the colors are random? Consider an arbitrary query halfspace and call the vertices of P inside it blue: can the convex hull of the blue points be computed in time linear in their number? More generally, can we quickly compute the blue hull without looking at the whole polytope? This paper considers several instances of hereditary computation and provides new results for them. In particular, we resolve an eight-year old open problem by showing how to split a convex polytope in linear expected time. Categories and Subject Descriptors F.2.2 [Nonnumerical Algorithms and Problems]: Geometrical problems and computations General Terms Algorithms, Theory Keywords convex polytope, half-space range searching, hereditary convex hulls
Bernard Chazelle, Wolfgang Mulzer
Added 28 May 2010
Updated 28 May 2010
Type Conference
Year 2009
Where COMPGEOM
Authors Bernard Chazelle, Wolfgang Mulzer
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