Extremal configurations and levels in pseudoline arrangements

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2748, Issue , 2003, Pages 127-139

  Sharir, Micha ^a,b   Smorodinsky, Shakhar ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

C (PROGRAMMING LANGUAGE); DIAMONDS; GRAPH THEORY;

DOUBLE WEDGE; DUAL-SETTING; GEOMETRIC GRAPHS; NEW RESULTS; PROJECTIVE PLANES; PSEUDO-LINE ARRANGEMENTS; PSEUDO-LINES; TOPOLOGICAL GRAPHS;

TOPOLOGY;

EID: 21144458909     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-45078-8_12     Document Type: Article

References (29)

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 (1998), 315-331.
2. P.K. Agarwal, B. Aronov, J, Pach, R. Pollack and M. Sharir, Quasi-planar graphs have a linear number of edges, Combinatorial 17 (1997), 1-9.
3. P.K. Agarwal, B. Aronov and M. Sharir, On the complexity of many faces in arrangements of pseudo-segments and of circles, Discrete Comput. Geom., The Goodman-Pollack festschrift, to appear.
4. P.K. Agarwal, E. Nevo, J. Pach, R. Pinchasi, M. Sharir and S. Smorodinsky, Lenses in arrangements of pseudodisks and their applications, J. ACM, to appear.
5. P.K. Agarwal and M. Sharir, Pseudoline arrangements: Duality, algorithms and applications, Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (2002), 781-790.
6. M. Ajtai, V. Chvátal, M. Newborn and E. Szemerédi, Crossing-free subgraphs, Ann. Discrete Math 12 (1982), 9-12.
7. G. Cairns and Y. Nikolayevsky, Bounds for generalized thrackles, Discrete Comput. Geom., 23 (2000), 191-206.
8. T.M. Chan, On levels in arrangements of curves, Proc. 41st IEEE Symp. Found. Comput. Sci. (2000), 219-227.
9. 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.
10. K. Clarkson and P. W. Shor Applications of random sampling in computational geometry, II Discrete Comput. Geom. 4 (1989), 387-421.
11. T. K. Dey, Improved bounds on planar k-sets and related problems, Discrete Comput. Geom. 19 (1998), 373-382.
12. T. Dey and J. Pach, Extremal problems for geometric hypergraphs, Discrete Comput. Geom. 19 (1998), 473-484.
13. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-verlag, Heidelberg, 1987.
14. I. Fáry, On straight-line representation of planar graphs, Acta Sciientiarum Mathematicarum (Szeged) 11 (1948), 229-233.
15. M. Katchalski and H. Last, On geometric graphs with no two edges in convex position, Discrete Comput. Geom. 19 (1998), 399-404.
16. F. T. Leighton, Complexity Issues in VLSI, MIT Press, Cambridge, MA, 1983.
17. F. Levi, Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade, Ber. Math-Phys. Kl. Sächs. Akad. Wiss. 78 (1926), 256-267.
18. L. Lovász, J, Pach and M. Szegedy, On Conway's thrackle conjecture, Discrete Comput. Geom. 18 (1997), 369-376.
19. J. S. B. Mitchell and J. O'Rourke. Computational geometry column 42. Internat. J. Comput. Geom. Appl. (2001).
20. Also in SIGACT News 32(3):63-72 (2001), Issue 120. See also: http://www.cs.smith.edu/ orourke/TOPP/
21. J. Pach, Geometric graph theory, in Surveys in Combinatorics (J.D. Lamb and D.A. Preece, eds.), London Mathematical Society Lecture Note Series 267, Cambridge University Press, 1999, 167-200.
22. M. Sharir and P.K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, New York, 1995.
23. L. Székely, Crossing numbers and hard Erdos problems in discrete geometry, Combinatorics, Probability and Computing 6 (1997), 353-358.
24. H. Tamaki and T. Tokuyama, A characterization of planar graphs by pseudo-line arrangements, Proc. 8th Annu. Internat. Sympos. Algorithms Comput. (ISAAC '97), Springer-Verlag Lecture Notes Comput. Sci., Vol. 1350, 1997, 133-142.
25. G. Tóth Point sets with many k-sets Discrete Comput. Geom. 26 (2001), 187-194.
26. W. T. Tutte, Toward a theory of crossing numbers, J. Combinat. Theory 8 (1970), 45-53.
27. P. Valtr, Graph drawings with no k pairwise crossing edges, Lecture Notes Comput. Sci. Springer-Verlag 1353 (1997), 205-218.
28. P. Valtr, On geometric graphs with no k pairwise parallel edges, Discrete Comput. Geom. 19 (1998), 461-469.
29. P. Valtr, Generalizations of Davenport-Schinzel sequences, in Contemporary Trends in Discrete Mathematics (J. Nesetril, J. Kratochvil, F.S. Roberts, R.L. Graham, Eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 49 (1999), 349-389.