Constructing Higher-Dimensional Convex Hulls at Logarithmic Cost per Face

@inproceedings{Seidel1986ConstructingHC,
  title={Constructing Higher-Dimensional Convex Hulls at Logarithmic Cost per Face},
  author={Raimund Seidel},
  booktitle={STOC},
  year={1986}
}
We exhibit a new approach for dealing with higher dimensional convex hull problems, such as enumerating all facets of the convex hull of a finite point set or constructing the facial lattice of such a convex hull. For fixed dimensions our new algorithms have worst case time complexity O(m 2 -tFlogm), where m is the size of the input point set and F is the size of the output produced. Such a dependence on the output size is desirable since F can range between ~(1) and O(mld/2|). Our time bound… CONTINUE READING

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