A general approach to d-dimensional geometric queries

@inproceedings{Yao1985AGA,
  title={A general approach to d-dimensional geometric queries},
  author={A. Yao and F. Yao},
  booktitle={STOC '85},
  year={1985}
}
  • A. Yao, F. Yao
  • Published in STOC '85 1985
  • Mathematics, Computer Science
  • It is shown that any bounded region in <italic>E</italic><supscrpt><italic>d</italic></supscrpt> can be divided into 2<supscrpt><italic>d</italic></supscrpt> subregions of equal volume in such a way that no hyperplane in <italic>E</italic><supscrpt><italic>d</italic></supscrpt> can intersect all 2<supscrpt><italic>d</italic></supscrpt> of the subregions. This theorem provides the basis of a data structure scheme for organizing <italic>n</italic> points in <italic>d</italic> dimensions. Under… CONTINUE READING
    163 Citations

    Topics from this paper

    Cutting hyperplane arrangements
    • 72
    Epsilon-nets and simplex range queries
    • 409
    • PDF
    How hard is halfspace range searching?
    • 55
    How to net a lot with little: small ε-nets for disks and halfspaces
    • 133
    Lines in space-combinators, algorithms and applications
    • 37
    Approximating extent measures of points
    • 332
    • PDF
    Polytope range searching and integral geometry
    • B. Chazelle
    • Mathematics, Computer Science
    • 28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
    • 1987
    • 18
    • PDF
    Quasi-optimal range searching in spaces of finite VC-dimension
    • 188
    • PDF
    Simplex Range Searching and Its Variants: A Review
    • 9
    • Highly Influenced
    • PDF