0 Logn Parallel Time Intersection And Union Algorithms for a Set of Planar Dis
0 Logn Parallel Time Intersection And Union Algorithms for a Set of Planar Dis
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Also, [Sharir, 83] shows how to construct the 2 Voronoi diagram of a set of n circular bodies, in time O(nlog n) and this can be used for detecting intersections between the circular bodies. [Brown, 79], shows O(nlogn) sequential algo- rithms, based on inversion transforms, which compute the (boun- dam of) the intersection and union of n circles in the plane (see also [Mehlhorn, 198'^]).
We consider here the problem of computing all the arcs and their sequence in the boundary of the intersectio...n (or the union of n circular discs in the plane. We first provide a nice cha- racterization of those boundaries. This leads to an O(logn) parallel time algorithm, running on the CREW PRAM model of pa- rallel computation. Our algorithm takes O(loglogn) time on a 3 CRCW PRAM. It needs n processors. Since O(nlogn) sequential algorithms for computing the intersection or union are known, our bound on the number of processors is by no means the best possible, (see [Brown, 79]). We also show that the boundary of the intersection of n circular discs in the plane, consists of at most 2n-2 arcs, for any n^2 .
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You can find similar books in the "Read Also" column, or choose other free books by T S Papatheodoro to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Also, [Sharir, 83] shows how to construct the 2 Voronoi diagram of a set of n circular bodies, in time O(nlog n) and this can be used for detecting intersections between the circular bodies. [Brown, 79], shows O(nlogn) sequential algo- rithms, based on inversion transforms, which compute the (boun- dam of) the intersection and union of n circles in the plane (see also [Mehlhorn, 198'^]).
We consider here the problem of computing all the arcs and their sequence in the boundary of the intersectio...n (or the union of n circular discs in the plane. We first provide a nice cha- racterization of those boundaries. This leads to an O(logn) parallel time algorithm, running on the CREW PRAM model of pa- rallel computation. Our algorithm takes O(loglogn) time on a 3 CRCW PRAM. It needs n processors. Since O(nlogn) sequential algorithms for computing the intersection or union are known, our bound on the number of processors is by no means the best possible, (see [Brown, 79]). We also show that the boundary of the intersection of n circular discs in the plane, consists of at most 2n-2 arcs, for any n^2 .
What to read after 0 Logn Parallel Time Intersection And Union Algorithms for a Set of Planar Dis?
You can find similar books in the "Read Also" column, or choose other free books by T S Papatheodoro to read onlineMoreLess
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