Non-Partitionable Point Sets

@article{Avis1984NonPartitionablePS,
  title={Non-Partitionable Point Sets},
  author={David Avis},
  journal={Inf. Process. Lett.},
  year={1984},
  volume={19},
  pages={125-129}
}
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

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

References

Publications referenced by this paper.
Showing 1-4 of 4 references

Comput

D E Willard, Polygon Retrieval, J Siam
Comput • 1982
View 3 Excerpts
Highly Influenced

3-space partition and its applications

F Yao
Proc. 15th STOC • 1983

Neighborly and cyclic polytopes

D Gale
Proc. Symp. on Pure Mathematics • 1963

Gray codes and paths on the n-cube

E N Gilbert
Bell Syst. Tech. J • 1958

Similar Papers

Loading similar papers…