D.T. Lee and F.P. Preparata. An improved algorithm for the rectangle enclosure problem. Journal of Algorithms, 3:218--224, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 [LP82], 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 ff different aspect ratios, we give an algorithm that runs in O(ffn log n k) time and uses O(n) space. 1 ....

....This author was supported by the ESPRIT Basic Research Actions Program, under contract No. 7141 (project ALCOM II) x DIMACS, Rutgers University, Piscataway, NJ 08855, U.S.A. E mail: bhaskar dimacs.rutgers.edu. 1 This problem finds applications in the computer aided design of VLSI circuits [LP82]. By mapping each rectangle R = l; r] Theta [b; t] to the point (l; b; Gammar; Gammat) in IR 4 , we can formulate this problem as a dominance problem: If p = p 1 ; p 2 ; p 3 ; p 4 ) and q = q 1 ; q 2 ; q 3 ; q 4 ) are points in IR 4 , then we say that p dominates q if p i q i for all i, ....

[Article contains additional citation context not shown here]

D.T. Lee and F.P. Preparata. An improved algorithm for the rectangle enclosure problem. Journal of Algorithms, 3:218--224, 1982.

....i.e. given a set S of objects, and a query object q, find a subset F of S such that for any f 2 F ; f q 6= We have then the rectangle enclosure searching problem, rectangle containment problem, segment intersection searching problem, etc. We list only a few references about these problems[22, 71, 82]. Janardan and Lopez[72] generalized the intersection searching in the following manner. The database is a collection of groups of objects, and the problem is to find all groups of objects intersecting a query object. A group is considered to be intersecting the query object if any object in the ....

D. T. Lee and F. P. Preparata, "An Improved Algorithm for the Rectangle Enclosure Problem," J. Algorithems, 3 (1982), 218-224.

....Ravi Janardan y Michiel Smid z Bhaskar Dasgupta xy Abstract We consider the problem of reporting the pairwise enclosures in 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 . Over a decade ago, Lee and Preparata [LP82] gave an O(n log 2 n k) time and O(n) space algorithm for these problems, where k is the number of reported pairs. Since that time, the question of whether there is a faster algorithm has remained an intriguing open problem. In this paper, we give an algorithm which runs in O(n log n log log ....

....an intriguing open problem. In this paper, we give an algorithm which runs in O(n log n log log n k log log n) time and uses O(n) space. Thus, although our result is not a strict improvement over the Lee Preparata algorithm for the full range of k, it is, nevertheless, the first result since [LP82] to make any progress on this long standing open problem. Our algorithm is based on the divide and conquer paradigm. The Department of Computer Science, University of Minnesota, Minneapolis, MN 55455, U.S.A. E mail: fpgupta,janardang cs.umn.edu. y The research of these authors was ....

[Article contains additional citation context not shown here]

D.T. Lee and F.P. Preparata. An improved algorithm for the rectangle enclosure problem. Journal of Algorithms, 3:218--224, 1982.

No context found.

D.T. Lee and F.P. Preparata, "An improved algorithm for the rectangle enclosure problem", Journal of Algorithms", 3 (1982) 218--224.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC