New upper bounds in Klee's measure problem

Mark H. Overmars, Chee Yap

Research output: Contribution to journalArticle

Abstract

New upper bounds for the measure problem of Klee are given which significantly improve the previous bounds for dimensions greater than two. An O(n d/2 log n, n) time-space upper bound is obtained and used to compute the measure of a set of n boxes in Euclidean d-space. The solution is based on new data structure, which is called an orthogonal partition tree. This structure has order applications as well.

Original languageEnglish (US)
Pages (from-to)1034-1045
Number of pages12
JournalSIAM Journal on Computing
Volume20
Issue number6
StatePublished - Dec 1991

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Data structures
Upper bound
D-space
Euclidean
Data Structures
Space-time
Partition

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

New upper bounds in Klee's measure problem. / Overmars, Mark H.; Yap, Chee.

In: SIAM Journal on Computing, Vol. 20, No. 6, 12.1991, p. 1034-1045.

Research output: Contribution to journalArticle

Overmars, MH & Yap, C 1991, 'New upper bounds in Klee's measure problem', SIAM Journal on Computing, vol. 20, no. 6, pp. 1034-1045.
Overmars, Mark H. ; Yap, Chee. / New upper bounds in Klee's measure problem. In: SIAM Journal on Computing. 1991 ; Vol. 20, No. 6. pp. 1034-1045.
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