
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Wei Chen, Koichi Wada, "On Computing the Upper Envelope of Segments in Parallel," IEEE Transactions on Parallel and Distributed Systems, vol. 13, no. 1, pp. 513, January, 2002.  
BibTex  x  
@article{ 10.1109/71.980023, author = {Wei Chen and Koichi Wada}, title = {On Computing the Upper Envelope of Segments in Parallel}, journal ={IEEE Transactions on Parallel and Distributed Systems}, volume = {13}, number = {1}, issn = {10459219}, year = {2002}, pages = {513}, doi = {http://doi.ieeecomputersociety.org/10.1109/71.980023}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Parallel and Distributed Systems TI  On Computing the Upper Envelope of Segments in Parallel IS  1 SN  10459219 SP5 EP13 EPD  513 A1  Wei Chen, A1  Koichi Wada, PY  2002 KW  Computational geometry KW  upper envelope KW  DavenportSchinzel sequence KW  visibility KW  convex hull KW  EREW PRAM model. VL  13 JA  IEEE Transactions on Parallel and Distributed Systems ER   
Given a collection of segments in the plane, if we regard the segments as opaque barriers, their upper envelope consists of the portions of the segments visible from point
[1] A. Aggarwal, B. Chazelle, L. Guibas, C. O'Dunlaing, and C. Yap, “Parallel Computational Geometry,” Algorithmica, no. 3, pp. 293327, 1988.
[2] T. Asano, T. Asano, L. Guibas, J. Hershberger, and H. Imai, “Visibility of Disjoint Polygons,” Algorithmica, no. 1, pp. 4963, 1986.
[3] M. Atallah, “Some Dynamic Computational Geometry Problems,” Computer Math. Applications, vol. 11, no. 12, pp. 11711181, 1985.
[4] L. Boxer and R. Miller, “Parallel Dynamic Computational Geometry,” Technical Report TR 8711, State University of New York, Buffalo, 1987.
[5] L. Boxer and R. Miller, “Common Intersections of Polygons,” Information Processing Letters, vol. 33, no. 5, pp. 249254, 1988.
[6] D.Z. Chen, W. Chen, K. Wada, and K. Kawaguchi, “Parallel Algorithms for Partitioning Sorted Sets and Related Problems,” Algorithmica, vol. 28, no. 2, pp. 217241, 2001.
[7] D.Z. Chen,“Efficient geometric algorithms on the EREWPRAM,” Proc. 28th Ann. Allerton Conf. on Comm., Control, and Computing, pp. 818827, 1990; also IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 1, pp. 4147, 1995.
[8] W. Chen, K. Nakano, T. Masuzawa, and N. Tokura, “Optimal Parallel Algorithms for Finding the Convex Hull of a Sorted Point Set,” IEICE Trans.,(Japanese) vol. J74DI, no. 12, pp. 814825, 1991.
[9] W. Chen and K. Wada, “Designing Efficient Parallel Algorithms with MultiLevel DivideandConquer,” IEICE Trans. Fundamentals of Electronics, Comm. and Computer Sciences, vol. E84A, no. 5, pp. 12011208, 2001.
[10] W. Chen, K. Wada, K. Kawaguchi, and D.Z. Chen, “A Parallel Method for Finding the Convex Hull of Discs,” Int'l J. Computational Geometry and Applications, vol. 8, no. 3, pp. 305319, 1998.
[11] F. Dehne, C. Kenyon, and A. Fabri, “Scalable and Architecture Independent Parallel Geometric Algorithms with High Probability Optimal Algorithm,” Proc. Sixth IEEE Symp. Parallel and Distributed Processing, pp. 586593, 1994.
[12] M.T. Goodrich, “Using Approximation Algorithms to Design Parallel Algorithms that May Ignore Processors Allocation,” Proc. 34nd Ann. Symp. Foundations of Computer Science, pp. 711722, 1991.
[13] D. Hart and M. Sharir, “Nonlinearity of DavenportSchinzel Sequences and of Generalized Path Compression Schemes,” Combinatorica, no. 6, pp. 151177, 1989.
[14] J. Hershberger, "Finding the Upper Envelope of n Line Segments in O(n log n) Time," Information Processing Letters, vol. 33, pp. 169174, 1989.
[15] J. Hershberger, “Upper Envelope Onion Peeling,” Compututational Geometry: Theory and Applications, vol. 2, no. 2, pp. 93110, 1989.
[16] J. J'aJ'a, An Introduction to Parallel Algorithms.New York: AddisonWesley, 1992.
[17] K. Kedem and M. Sharir, “An Efficient MotionPlanning Algorithm for a Convex Polygonal Object in TwoDimensional Polygonal Space,” Discrete Computational Geometry, vol. 5, no. 1, pp. 43755, 1990.
[18] P.D. MacKenzie and Q. Stout, “Asymptotically Efficient Hypercube Algorithms for Computational Geometry,” Proc. Third Symp. Frontiers of Massively Parallel Computation, pp. 811, 1990.
[19] E.A. Ramos, “Construction of 1d Lower Envelopes and Applications,” Proc. 13th Ann. Symp. Computational Geometry, pp. 5766, 1997.
[20] J.H. Reif, “An Optimal Parallel Algorithm for Integer Sorting,” Proc. 26th Ann. Symp. Foundations of Computer Science, pp. 496504, 1985.
[21] G. Sakas and J. Hartig, "Interactive Visualization of Large Scalar Voxel Fields," A. Kaufman and E.G. Nielson, eds., IEEE Visualization '92 Proc., pp. 2936,Boston, Mass., Oct. 1992.