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Efficient plane sweeping in parallel
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Source Annual Symposium on Computational Geometry archive
Proceedings of the second annual symposium on Computational geometry table of contents
Yorktown Heights, New York, United States
Pages: 216 - 225  
Year of Publication: 1986
ISBN:0-89791-194-6
Authors
M J Atallah  Department of Computer Sciences, Purdue University, West Lafayette, IN
M T Goodrich  Department of Computer Sciences, Purdue University, West Lafayette, IN
Sponsors
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
Publisher
ACM  New York, NY, USA
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Downloads (6 Weeks): 8,   Downloads (12 Months): 27,   Citation Count: 5
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ABSTRACT

We present techniques which result in improved parallel algorithms for a number of problems whose efficient sequential algorithms use the plane-sweeping paradigm. The problems for which we give improved algorithms include intersection detection, trapezoidal decomposition, triangulation, and planar point location. Our technique can be used to improve on the previous time bound while keeping the space and processor bounds the same, or improve on the previous space bound while keeping the time and processor bounds the same. We also give efficient parallel algorithms for visibility from a point, 3-dimensional maxima, multiple range-counting, and rectilinear segment intersection counting. We never use the AKS sorting network in any of our algorithms.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
A. Aggarwal, B. Chazelle, L. Guibas, C. O'Dfinlaing, and C. Yap, gParallel Computational Geometry," Pro~. ~5th IEEE $~mp. Found. of Comp. $ci., 1985, 468--477.
 
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M.J. Agallah and M.T. Goodrich, gEfficient Plane Sweeping in Paranel," Purdue University Computer Science Tech. Report CSD-TR-56a, March 1986.
 
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B. Chazelle and J. Incerpi, "Triangulating a Polygon by Divide-and-Conquer," Proc. of ~1st Allerton Con/. on Comm. Control, and Comp., 1983, 447-456.
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B. Chazelle and L.J. Guibas, "Fractional Cascading: I. A Data Structuring Technique," manuscript.
 
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H. El Gindy and D. Avis, "A Linear Algorithm for Computing the Visibility Polygon from a Point," J. of Algorithms, Vol. 2, 1981, 186-197.
 
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M.T. Goodrich, "An Optimal Parallel Algorithm For the All Nearest-Neighbor Problem for a Convex Polygon," Purdue University Computer Science Tech. Report CSD-TR- 533, August 1985.
 
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D. Kirkpatrick, "Optimal Search in Planar Subdivision," SIAM Jour. on Comp., Vol. 12, No. 1, Feb. 1983, 28-35.
 
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C. Kruskal, L. Rudolph, and M. Snir, "The Power of Parallel Prefix,~ Proc. 1985 Int. Conf. on Parallel Proc., 180-185.
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D.T. Lee and F.P. Preparata, ~Computational Geometry-- A Survey," IEEE Trans. on Computers, Vol. C-33, No. 12, December 1984, 872-1101.
 
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G. Lueker and D. Willard, "A Data Structure for Dynamic Range Queriesf lnfo. Proc. Letters, Vol. 15, No. 5, Decembet 1982, 209-213.
 
18
M.H. Overmars and J. Van Leeuwen, "Maintenance of Configurations in the Plane," Jour. of Cornp. and Sys. Sci., Vol. 23, 1981, 166-204.
 
19
M. Shamos and D. Hoey, "Geometric Intersection Problems," Proc. 17th iEEE S~lrnp. Found. of Comp. Sci., 1976, 208-215.
 
20
L. Valiant, "Parallelism in Comparison Problems,~ SIAM Jour. on Cornp., Vol. 4, No. 3, Sept. 1975, 348-355.


Collaborative Colleagues:
M J Atallah: colleagues
M T Goodrich: colleagues