On levels in arrangements of curves, II: A simple inequality and its consequences

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2003, Pages 544-550

  Chan, Timothy M ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; CURVE FITTING; GRAPH THEORY; QUADRATIC PROGRAMMING;

CUTTING CURVES; SUBQUADRATIC COMPLEXITY;

COMPUTER SCIENCE;

EID: 0344118851     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (33)

1. P. K. Agarwal, B. Aronov, T. M. Chan, and M. Sharir. On levels in arrangements of lines, segments, planes, and triangles. Discrete Comput. Geom., 19:315-331, 1998. (Preliminary version in Proc. 13th ACM Sympos. Comput. Geom., pages 30-38, 1997).
2. P. K. Agarwal, B. Aronov, and M. Sharir. On the complexity of many faces in arrangements of circles. To appear in Discrete and Computational Geometry: The Goodman-Pollack Festschrift (B. Aronov, S. Basu, J. Pach, M. Sharir, eds.), Springer-Verlag, Berlin. (Also in Proc. 42nd IEEE Sympos. Found. Comput. Sci., pages 74-83, 2001).
3. P. K. Agarwal, D. Eppstein, L. J. Guibas, and M. R. Henzinger. Parametric and kinetic minimum spanning trees. In Proc. 39th IEEE Sympos. Found. Comput. Sci., pages 596-605, 1998.
4. P. K. Agarwal, E. Nevo, J. Pach, R. Pinchasi, M. Sharir, and S. Smorodinsky. Lenses in arrangements of pseudo-circles and their applications. J. ACM, to appear. (Preliminary version in Proc. 18th ACM Sympos. Comput. Geom., pages 123-132, 2002).
5. P. K. Agarwal and M. Sharir. Arrangements and their applications. In Handbook of Computational Geometry (J. Urrutia and J. Sack, eds.), North-Holland, pages 49-119, 2000.
6. N. Alon and E. Györi. The number of small semispaces of a finite set of points in the plane. J. Combin. Theory Ser. A, 41:154-157, 1986.
7. A. Andrzejak and E. Welzl. k-sets and j-facets: a tour of discrete geometry. Manuscript, 1997.
8. T. M. Chan. Remarks on k-level algorithms in the plane. Manuscript, 1999.
9. T. M. Chan. On levels in arrangements of curves. Discrete Comput. Geom., 29:375-393, 2003. (Preliminary version in Proc. 41st IEEE Sympos. Found. Comput. Sci., pages 219-227, 2000).
10. T. M. Chan. Low-dimensional linear programming with violations. In Proc. 43rd IEEE Sympos. Found. Comput. Sci., pages 570-579, 2002.
11. B. Chazelle and F. P. Preparata. Halfspace range search: an algorithmic application of k-sets. Discrete Comput. Geom., 1:3-93, 1986.
12. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387-421, 1989.
13. T. K. Dey. Improved bounds on planar k-sets and related problems. Discrete Comput. Geom., 19:373-382, 1998.
14. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin, 1987.
15. D. Eppstein. Geometric lower bounds for parametric matroid optimization. Discrete Comput. Geom., 20:463-476, 1998.
16. P. Erdös, L. Lovász, A. Simmons, and E. Straus. Dissection graphs of planar point sets. In A Survey of Combinatorial Theory (J. N. Srivastava, ed.), North-Holland, Amsterdam, Netherlands, pages 139-154, 1973.
17. J. E. Goodman and R. Pollack, On the number of k-subsets of a set of n points in the plane. J. Combin. Theory Ser. A, 36:101-104, 1984.
18. D. Halperin. Arrangements. In Handbook of Discrete and Computational Geometry (J. E. Goodman and J. O'Rourke, eds.), pages 389-412, CRC Press, 1997.
19. N. Katoh, H. Tamaki, and T. Tokuyama. Parametric polymatroid optimization and its geometric applications. Int. J. Comput. Geom. Appl., 12:429-443, 2002.
20. C.-Y. Lo, J. Matoušek, and W. L. Steiger. Algorithms for ham-sandwich cuts. Discrete Comput. Geom., 11:433-452, 1994.
21. L. Lovász. On the number of halving lines. Ann. Univ. Sci. Budapest, Eötvös, Sec. Math., 14:107-108, 1971.
22. J. Matoušek. Lectures on Discrete Geometry. Springer-Verlag, 2002.
23. J. Pach and P. K. Agarwal. Combinatorial Geometry. Wiley-Interscience, New York, 1995.
24. J. Pach, W. Steiger, and E. Szemerédi. An upper bound on the number of planar k-sets. Discrete Comput. Geom., 7:109-123, 1992.
25. R. Pinchasi and R. Radoičić. Topological graphs with no self-intersecting cycle of length 4. In Proc. 19th ACM Sympos. Comput. Geom., pages 98-103, 2003.
26. M. Sharir. On k-sets in arrangements of curves and surfaces. Discrete Comput. Geom., 6:593-613, 1991.
27. M. Sharir and P. K. Agarwal. Davenport-Schinzel Sequences and Their Geometric Applications. Cambridge University Press, New York, 1995.
28. M. Sharir, S. Smorodinsky, and G. Tados. An improved bound for k-sets in three dimensions. Discrete Comput. Geom., 26:195-204, 2001.
29. B. Tagansky. A new technique for analyzing substructures in arrangements of piecewise linear surfaces. Discrete Comput. Geom., 16:455-479, 1996.
30. H. Tamaki and T. Tokuyama. A characterization of planar graphs by pseudo-line arrangements. In Proc. 8th Int. Sympos. Algorithms and Computation, Lect. Notes in Comput. Sci., vol. 1350, Springer-Verlag, pages 123-132, 1997.
31. H. Tamaki and T. Tokuyama. How to cut pseudoparabolas into segments. Discrete Comput. Geom., 19:265-290, 1998.
32. G. Toth. Point sets with many k-sets. Discrete Comput. Geom., 26:187-194, 2001.
33. E. Welzl. More on k-sets of finite sets in the plane. Discrete Comput. Geom., 1:95-100, 1986.