A general approach to d-dimensional geometric queries

  title={A general approach to d-dimensional geometric queries},
  author={Andrew Chi-Chih Yao and F. Frances Yao},
  booktitle={STOC '85},
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… 
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