Cutting circles into pseudo-segments and improved bounds for incidences

Discrete and Computational Geometry

Volumn 28, Issue 4, 2002, Pages 475-490

  Aronov, Boris ^a   Sharir, Micha ^b,c  

^a POLYTECHNIC UNIVERSITY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036883301     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-001-0084-1     Document Type: Article

References (21)

1. P.K. Agarwal and J. Malouaek, On range searching with semialgebraic sets, Discrete Comput. Geom. 11 (1994), 393-418.
2. P. Agarwal and M. Sharir, On the number of congruent simplices in a point set, Five. 17th ACM Symp. Comput. Geom. (2001), pp. 1-10. Also to appear in Discrete Comput. Geom.
3. M. Ajtai, V. Chvátal, M.M. Newborn, and E. Szemerédi, Crossing-free subgraphs, Ann. Discrete Math. 12 (1982), 9-12.
4. N. Alon, H. Last, R. Pinchasi, and M. Sharir, On the complexity of arrangements of circles in the plane, Discrete Comput. Geom. 26 (2001), 465-492.
5. T.M. Chan, On levels in arrangements of curves, Proc. 41st IEEE Symp, Found. Comput. Sci. (2000), pp. 219-227.
6. B. Chazelle and J. Friedman, A deterministic view of random sampling and its use in geometry, Combinatorica 10 (1990), 229-249.
7. K. Clarkson, H. Edelsbrunner, L. Guibas, M. Sharir, and E. Welzl, Combinatorial complexity bounds for arrangements of curves and spheres, Discrete Comput. Geom. 5 (1990), 99-160.
8. K. Clarkson and P. Shor, Applications of random sampling in computational geometry, II, Discrete Comput. Geom. 4 (1989), 387-421.
9. T. Dey and J. Pach, Extremal problems for geometric hypergraphs, Discrete Comput. Geom. 19 (1998), 473-484.
10. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, 1987.
11. S. Har-Peled, The Complexity of Many Cells in the Overlay of Many Arrangements, M.Sc. Thesis, Dept. Computer Science, Tel Aviv University, 1995. See also; Multicolor combination lemmas, Comput. Geom. Theory Appl. 12 (1999), 155-176.
12. S. Har-Peled, The Complexity of Many Cells in the Overlay of Many Arrangements, M.Sc. Thesis, Dept. Computer Science, Tel Aviv University, 1995. See also; Multicolor combination lemmas, Comput. Geom. Theory Appl. 12 (1999), 155-176.
13. F.T. Leighton, Complexity Issues in VLSI, Foundations of Computing Series, MIT Press, Cambridge, MA, 1983.
14. J. Matoušek, Efficient partition trees, Discrete Comput. Geom. 8 (1992), 315-334.
15. J. Pach and P.K. Agarwal. Combinatorial Geometry. Wiley-Interscience, New York, 1995.
16. J. Pach and M. Sharir, On the number of incidences between points and curves. Combinatorics Probab. Comput. 7 (1998), 121-127.
17. R. Pinchasi, Gallai-Sylvester theorem for pairwise-intersecting unit circles in the plane, Manuscript, 1999.
18. M. Sharir and P.K. Agarwal, Davenport Schinzel Sequences and Their Geometric Applications, Cambridge University Press, New York, 1995.
19. J. Solymosi and C. Toth, Distinct distances in the plane, Discrete Comput. Geom. 25 (2001), 629-634.
20. L. Székely, Crossing numbers and hard Erdos problems in discrete geometry. Combinatorics Probab. Comput. 6(1997), 353-358.
21. H. Tamaki and T. Tokuyama, How to cut pseudo-parabolas into segments, Discrete Comput. Geom. 19 (1998). 265-290.