Robustness issues in geometric algorithms

Applied Computational Geometry Towards Geometric Engineering - Lecture Notes in Computer Science ◽

10.1007/bfb0014476 ◽

1996 ◽

pp. 9-14 ◽

Cited By ~ 6

Author(s):

Steven Fortune

Keyword(s):

Geometric Algorithms

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Geometric algorithms for message filtering in decentralized virtual environments

Proceedings of the 1999 symposium on Interactive 3D graphics - SI3D '99 ◽

10.1145/300523.300527 ◽

1999 ◽

Cited By ~ 11

Author(s):

Yohai Makbily ◽

Craig Gotsman ◽

Reuven Bar-Yehuda

Keyword(s):

Virtual Environments ◽

Geometric Algorithms

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Parallel geometric algorithms on a mesh-connected computer

Algorithmica ◽

10.1007/bf01840383 ◽

1990 ◽

Vol 5 (1-4) ◽

pp. 155-177 ◽

Cited By ~ 32

Author(s):

C. S. Jeong ◽

D. T. Lee

Keyword(s):

Geometric Algorithms

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Sublinear Geometric Algorithms

SIAM Journal on Computing ◽

10.1137/s009753970444572x ◽

2005 ◽

Vol 35 (3) ◽

pp. 627-646 ◽

Cited By ~ 20

Author(s):

Bernard Chazelle ◽

Ding Liu ◽

Avner Magen

Keyword(s):

Geometric Algorithms

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GEOMETRIC ALGORITHMS FOR THE CONSTRAINED 1-D K-MEANS CLUSTERING PROBLEMS AND IMRT APPLICATIONS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054109006619 ◽

2009 ◽

Vol 20 (02) ◽

pp. 361-377

Author(s):

DANNY Z. CHEN ◽

MARK A. HEALY ◽

CHAO WANG ◽

BIN XU

Keyword(s):

Radiation Therapy ◽

Treatment Planning ◽

Intensity Modulated Radiation Therapy ◽

Geometric Algorithms ◽

Maximum Difference ◽

Continuous Version ◽

Heuristic Approaches ◽

Clustering Problem ◽

Intensity Modulated ◽

Clustering Problems

In this paper, we present efficient geometric algorithms for the discrete constrained 1-D K-means clustering problem and extend our solutions to the continuous version of the problem. One key clustering constraint we consider is that the maximum difference in each cluster cannot be larger than a given threshold. These constrained 1-D K-means clustering problems appear in various applications, especially in intensity-modulated radiation therapy (IMRT). Our algorithms improve the efficiency and accuracy of the heuristic approaches used in clinical IMRT treatment planning.

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