
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
F. Saxena, P.C.P. Bhatt, V.C. Prasad, "Efficient VLSI Parallel Algorithm for Delaunay Triangulation on Orthogonal Tree Network in Two and Three Dimensions," IEEE Transactions on Computers, vol. 39, no. 3, pp. 400404, March, 1990.  
BibTex  x  
@article{ 10.1109/12.48871, author = {F. Saxena and P.C.P. Bhatt and V.C. Prasad}, title = {Efficient VLSI Parallel Algorithm for Delaunay Triangulation on Orthogonal Tree Network in Two and Three Dimensions}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {3}, issn = {00189340}, year = {1990}, pages = {400404}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.48871}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Efficient VLSI Parallel Algorithm for Delaunay Triangulation on Orthogonal Tree Network in Two and Three Dimensions IS  3 SN  00189340 SP400 EP404 EPD  400404 A1  F. Saxena, A1  P.C.P. Bhatt, A1  V.C. Prasad, PY  1990 KW  VLSI parallel algorithm; Delaunay triangulation; orthogonal tree network; worst case time complexity; tetrahedra; logarithmic delay model; computational complexity; parallel algorithms; trees (mathematics). VL  39 JA  IEEE Transactions on Computers ER   
An algorithm with worst case time complexity O(log/sup 2/N) in two dimensions and O(m/sup 1/2/log N) in three dimensions with N input points and m as the number of tetrahedra in triangulation is given. Its AT/sup 2/ VLSI complexity on Thompson's logarithmic delay model, (1983) is O(N/sup 2/log/sup 6/N) in two dimensions and O(m/sup 2/Nlog/sup 4/ N) in three dimensions.
[1] A. Aggarwal, B. Chazelle, L. Guibas, C. O. Dunlaing, and C. Yap, "Parallel computational geometry," manuscript, 1987.
[2] M. J. Atallah, R. Cole, and M. T. Goodrich, "Cascading divideandconquer: A technique for designing parallel algorithms," manuscript, 1987.
[3] J.D. Boissonnat, "Geometric Structures for ThreeDimensional Shape Representation,"ACM Trans. Graphics, Jan. 1987, pp. 266286.
[4] J. C. Cavendish, "Automatic triangulation of arbitrary planar domains for finite element method,"Int. J. Numer. Methods Eng., vol. 8, pp. 679696, 1974.
[5] R. C. Chang and R. C. T. Lee, "AnO(nlogn) minimal spanning tree algorithm for n points in the plane,"BIT, vol. 26, pp. 716, 1986.
[6] A. L. Chow, "Parallel algorithms for geometric problems," Ph.D. dissertation, Dep. Comput. Sci., Univ. of Illinois, Urbana, IL, 1980.
[7] D. Dadoun and D. G. Kirkpatrick, "Parallel processing for efficient subdivision search," inProc. ACM Symp. Computational Geometry, 1987, pp. 205214.
[8] H. Edelsbrunner,Algorithms in Combinatorial Geometry, SpringerVerlag, New York, 1987.
[9] D. A. Field, "Implementing Watson's algorithm in 3dimensions," inProc. ACM Symp. Computational Geometry, 1986, pp. 246259.
[10] L. Guibas and J. Stolfi, "Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams,"ACM Trans. Graphics, Vol. 4, No. 2, April 1985, pp. 74123.
[11] D. J. Kuck,The Structure of Computers and Computations, vol. 1. New York: Wiley, 1978.
[12] M. Lu, "Constructing the Voronoi diagram on a mesh connected computer," inProc. Int. Conf. Parallel Processing, 1986, pp. 806811.
[13] D. Nath, S. N. Maheshwari, and P. C. P. Bhatt, "Efficient VLSI networks for parallel processing based on orthogonal trees,"IEEE Trans. Comput., vol. C32, pp. 569581, June 1983.
[14] F. P. Preparata, "A meshconnected areatime optimal VLSI multiplier of large integers,"IEEE Trans. Comput., vol. C32, pp. 194198, Feb. 1983.
[15] F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: SpringerVerlag, 1985.
[16] S. Saxena, P. C. P. Bhatt, and V. C. Prasad, "Parallel algorithms for Delaunay triangulation in two and three dimensions," Tech. Rep. JUN/1/87, Comput. Sci. Eng., Indian Institute of Technology, New Delhi.
[17] J. M. Smith, D. T. Lee, and J. S. Liebman, "AnO(nlogn) heuristic for Steiner minimal tree problem on the Euclidean metric,"Networks, vol. 11, pp. 2329, Spring 1981.
[18] C. D. Thompson, "The VLSI complexity of sorting,"IEEE Trans. Comput., vol. C32, pp. 11711184, Dec. 1983.
[19] C. A. Wang and Y. H. Tsin, "AnO(logN) time parallel algorithm for triangulating a set of points in the plane,"IPL, vol. 25, pp. 5560, Apr. 6, 1987.