### 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 language | English (US) |
---|---|

Pages (from-to) | 1034-1045 |

Number of pages | 12 |

Journal | SIAM Journal on Computing |

Volume | 20 |

Issue number | 6 |

State | Published - Dec 1991 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*SIAM Journal on Computing*,

*20*(6), 1034-1045.

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

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 20, no. 6, pp. 1034-1045.

}

TY - JOUR

T1 - New upper bounds in Klee's measure problem

AU - Overmars, Mark H.

AU - Yap, Chee

PY - 1991/12

Y1 - 1991/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0026406169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026406169&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0026406169

VL - 20

SP - 1034

EP - 1045

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 6

ER -