@techreport{GuptaJanardanSmidDasgupta94,
TITLE = {The rectangle enclosure and point-dominance problems revisited},
AUTHOR = {Gupta, Prosenjit and Janardan, Ravi and Smid, Michiel and Dasgupta, Bhaskar},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/94-142},
NUMBER = {MPI-I-94-142},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {1994},
DATE = {1994},
ABSTRACT = {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},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}