Non-Partitionable Point Sets

  title={Non-Partitionable Point Sets},
  author={David Avis},
  journal={Inf. Process. Lett.},
Let S be a finite set of n points in d-dimensional space. S is e.(n)-partitionable if there exists a set of d mutually intersecting hyperplanes that divide d-space into 2d open regions, no 2d 1 of which together contain more than o(n) points of S. Willard (1982) has shown that every set in 2-space is :n-partitionable. Yao (1983) has shown that every set in 3-space is gn-partitionable. It is shown here that there exist sets S of arbitrary cardinality in d-space, d 2 5, for which d2 +l open… CONTINUE READING

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