The smallest enclosing ball of balls: Combinatorial structure and algorithms

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2003, Pages 292-301

  Fischer, Kaspar ^a   Gärtner, Bernd ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Distance to convex hull; Minimal covering ball; Minimum volume sphere; Unique sink orientation

Indexed keywords

ALGORITHMS; NUMERICAL METHODS; SET THEORY;

COMBINATORIAL STRUCTURES;

PROBLEM SOLVING;

EID: 0038714744     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty. Nonlinear programming: theory and applications. Wiley, 1979.
2. M. Berger. Geometry (vols. 1-2). Springer-Verlag, 1987.
3. B. Chazelle and J. Matoušek. On linear-time deterministic algorithms for optimization problems in fixed dimension. J. Algorithms, 21:579-597, 1996.
4. V. Chvátal. Linear programming. W. H. Freeman, New York, NY, 1983.
5. M. E. Dyer. Linear time algorithms for two- and three-variable linear programs. SIAM J. Comput., 13:31-45, 1984.
6. M. E. Dyer. A class of convex programs with applications to computational geometry. In Proc. 8th Annu. ACM Sympos. Comput. Geom., pages 9-15, 1992.
7. B. Gärtner. A subexponential algorithm for abstract optimization problems. SIAM J. Comput, 24(5):1018-1035, 1995.
8. B. Gärtner. Fast and robust smallest enclosing balls. In Proc. 7th Annual European Symposium on Algorithms (ESA), volume 1643 of Lecture Notes Comput. Sci., pages 325-338. Springer-Verlag, 1999.
9. B. Gärtner and E. Welzl. Explicit and implict enforcing - randomized optimization. In Computational Discrete Mathematics, volume 2122 of LNCS, pages 25-46. Springer-Verlag, 2001.
10. T. H. Hopp and C. P. Reeve. An algorithm for computing the minimum covering sphere in any dimension. Technical Report NISTIR 5831, National Institute of Standards and Technology, 1996.
11. M. Karavelas and I. Emiris. Predicates for the planar additively weighted Voronoi diagram. ECG Technical Report ECG-TR-122201-01, Sophia-Antipolis, 2002.
12. P. Kumar, J. S. B. Mitchell, and E. A. Yildirim. Computing core-sets and approximate smallest enclosing hyperspheres in high dimensions. To appear in the Proceedings of ALENEX'03.
13. +-tree: an improved index structure for similarity searches in a high-dimensional feature space. In Proc. 5th Storage and Retrieval for Image and Video Databases SPIE, volume 3022, pages 110-120, 1997.
14. J. Matoušek, M. Sharir, and E. Welzl. A subexponential bound for linear programming. Algorithmica, 16:498-516, 1996.
15. 3 and related problems. SIAM J. Comput., 12(4):759-776, 1983.
16. N. Megiddo. Linear programming in linear time when the dimension is fixed. J. ACM, 31:114-127, 1984.
17. N. Megiddo. On the ball spanned by balls. Discrete Comput. Geom., 4:605-610, 1989.
18. R. Seidel, e-mail communication, 1997.
19. T. Szabó and E. Welzl. Unique sink orientations of cubes. In Proc. 42nd. annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 547-555, 2001.
20. E. Welzl. Smallest enclosing disks (balls and ellipsoids). In H. Maurer, editor, New Results and New Trends in Computer Science, volume 555 of Lecture Notes Comput. Sci., pages 359-370. Springer-Verlag, 1991.
21. H.-M. Will. Computation of additively weighted Voronoi cells for applications in molecular biology. PhD thesis, ETH Zürich, 1998.