# MPI-I-94-142

## The rectangle enclosure and point-dominance problems revisited

### Gupta, Prosenjit and Janardan, Ravi and Smid, Michiel and Dasgupta, Bhaskar

**MPI-I-94-142**. August** **1994, 16 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

We consider the problem of reporting the pairwise enclosures

among a set of $n$ axes-parallel rectangles in $\IR^2$,

which is equivalent to reporting dominance pairs in a set

of $n$ points in $\IR^4$. For more than ten years, it has been

an open problem whether these problems can be solved faster than

in $O(n \log^2 n +k)$ time, where $k$ denotes the number of

reported pairs. First, we give a divide-and-conquer algorithm

that matches the $O(n)$ space and $O(n \log^2 n +k)$ time

bounds of the algorithm of Lee and Preparata,

but is simpler.

Then we give another algorithm that uses $O(n)$ space and runs

in $O(n \log n \log\log n + k \log\log n)$ time. For the

special case where the rectangles have at most $\alpha$

different aspect ratios, we give an algorithm tha

Acknowledgement:** **

References to related material:

To download this research report, please select the type of document that fits best your needs. | Attachement Size(s): |

MPI-I-94-142.pdf | 72 KBytes; 203 KBytes |

Please note: If you don't have a viewer for PostScript on your platform, try to install GhostScript and GhostView |

**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1994-142

**BibTeX**
`@TECHREPORT{``GuptaJanardanSmidDasgupta94``,`

` AUTHOR = {Gupta, Prosenjit and Janardan, Ravi and Smid, Michiel and Dasgupta, Bhaskar},`

` TITLE = {The rectangle enclosure and point-dominance problems revisited},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-94-142},`

` MONTH = {August},`

` YEAR = {1994},`

` ISSN = {0946-011X},`

`}`