Line-Segment Intersection Made In-Place

2005 ◽  
pp. 146-157 ◽  
Author(s):  
Jan Vahrenhold
Keyword(s):  
Line Segment ◽  
Line Segment Intersection ◽  
Made In

scholarly journals Line-segment intersection made in-place

2007 ◽  
Vol 38 (3) ◽  
pp. 213-230 ◽  
Author(s):  
Jan Vahrenhold
Keyword(s):  
Line Segment ◽  
Line Segment Intersection ◽  
Made In

Line Segment Intersection

1997 ◽  
pp. 19-43
Author(s):  
Mark de Berg ◽  
Marc van Kreveld ◽  
Mark Overmars ◽  
Otfried Schwarzkopf
Keyword(s):  
Line Segment ◽  
Line Segment Intersection

scholarly journals Line Segment Intersection Testing

Computing ◽  
2005 ◽  
Vol 75 (4) ◽  
pp. 337-357 ◽  
Author(s):  
Y.-K. Zhu ◽  
J.-H. Yong ◽  
G.-Q. Zheng
Keyword(s):  
Line Segment ◽  
Line Segment Intersection

Line Segment Intersection

2000 ◽  
pp. 19-43 ◽  
Author(s):  
Mark de Berg ◽  
Marc van Kreveld ◽  
Mark Overmars ◽  
Otfried Cheong Schwarzkopf
Keyword(s):  
Line Segment ◽  
Line Segment Intersection

SCALABLE ALGORITHMS FOR BICHROMATIC LINE SEGMENT INTERSECTION PROBLEMS ON COARSE GRAINED MULTICOMPUTERS

1996 ◽  
Vol 06 (04) ◽  
pp. 487-506 ◽  
Author(s):  
ANDREAS FABRI ◽  
OLIVIER DEVILLERS
Keyword(s):  
Line Segment ◽  
Time Complexity ◽  
Coarse Grained ◽  
Log P ◽  
Scalable Algorithms ◽  
Interprocessor Communication ◽  
Additional Time ◽  
Sequential Computation ◽  
Communication Time ◽  
Line Segment Intersection

We present output-sensitive scalable parallel algorithms for bichromatic line segment intersection problems for the coarse grained multicomputer model. Under the assumption that n≥p2, where n is the number of line segments and p the number of processors, we obtain an intersection counting algorithm with a time complexity of [Formula: see text], where Ts(m, p) is the time used to sort m items on a p processor machine. The first term captures the time spent in sequential computation performed locally by each processor. The second term captures the interprocessor communication time. An additional [Formula: see text] time in sequential computation is spent on the reporting of the k intersections. As the sequential time complexity is O(n log n) for counting and an additional time O(k) for reporting, we obtain a speedup of [Formula: see text] in the sequential part of the algorithm. The speedup in the communication part obviously depends on the underlying architecture. For example for a hypercube it ranges between [Formula: see text] and [Formula: see text] depending on the ratio of n and p. As the reporting does not involve more interprocessor communication than the counting, the algorithm achieves a full speedup of p for k≥ O( max (n log n log p, n log 3 p)) even on a hypercube.

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