Pseudo-line arrangements: Duality, algorithms, and applications

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn 06-08-January-2002, Issue , 2002, Pages 800-809

  Agarwal, Pankaj K ^a   Sharir, Micha ^b,c  

^a Duke University   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL EFFICIENCY;

APPROPRIATE MODELS; CIRCULAR ARC; DYNAMIC DATA STRUCTURE; JORDAN CURVES; K POINTS; PSEUDO-LINE ARRANGEMENTS; PSEUDO-LINES;

ALGORITHMS;

EID: 84968877244     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. P. K. Agarwal, Partitioning arrangements of lines: II. Applications, Discrete Comput. Geom., 5 (1990), 533-573.
2. P. K. Agarwal, B-Aronov and M. Sharir, On the complexity of many faces in arrangements of pseudo-segments and of circles, to appear in Proc. 42nd Annual Sympos. Foundations of Computer Science, 2001.
3. P. K. Agarwal, B. Aronov, M. Sharir, and S. Suri, Selecting distances in the plane, Algorithmica, 9 (1993), 495-514.
4. P. K. Agarwal and J. Erickson, Geometric range searching and its relatives, in: Advances in Discrete and Computational Geometry (B. Chazelle, J. E. Goodman, and R. Pollack, eds.), Contemporary Mathematics, Vol. 223, American Mathematical Society, Providence, RI, 1999, pp. 1-56.
5. P. K. Agarwal and J. Matousek, On range searching with semialgebraic sets, Discrete Comput. Geom., 11 (1994), 393-418.
6. P. K. Agarwal and J. Matousek, Dynamic half-space range reporting and its applications, Algorithmica, 13 (1995), 325-345.
7. P. K. Agarwal, E. Nevo, J. Pach, R. Pinchasi, M. Sharir, and S. Smorodinsky, Lenses in arrangements of pseudo-circles and their applications, manuscript, 2001.
8. P. K. Agarwal and M. Sharir, Arrangements and their applications, in: Handbook of Computational Geometry (J.-R. Sack and J. Urrutia, eds.), Elsevier Science Publishers B.V. North-Holland, Amsterdam, 2000, pp. 49-119.
9. B. Aronov and M. Sharir, Cutting circles into pseudo-segments and improved bounds on incidences, Discrete Comput. Geom., to appear.
10. S. A. Burr, B. Griinbaum, and N. J. A. Sloane, The orchard problem, Geom. Dedicata, 2 (1974), 397-424.
11. T.M. Chan, On levels in arrangements of curves, Proc. 41st IEEE Symp. Found. Comput. Sci., 2000, 219-227.
12. B. Chazelle, Cutting hyperplanes for divide-and-conquer, Discrete Comput. Geom., 9 (1993), 145-158.
13. H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg, 1987.
14. H. Edelsbrunner, L. Guibas and M. Sharir, The complexity and construction of many faces in arrangements of lines and of segments, Discrete Comput. Geom. 5 (1990), 161-196.
15. J. E. Goodman, Proof of a conjecture of Burr, Grünbaum and Sloane, Discrete Math., 32 (1980), 27-35.
16. J. E. Goodman, Pseudoline arrangements, in Handbook of Discrete and Computational Geometry (J.E. Goodman and J. O'Rourke, eds.), CRC Press, Boca Raton, FL, 1987, pp. 83-109.
17. J. E. Goodman and R. Pollack, On the combinatorial classification of nondegenerate configurations in the plane, J. Combin. Theory Ser. A, 29 (1980), 220-235.
18. J. E. Goodman and R. Pollack, A theorem of ordered duality, Geom. Dedicata, 12 (1982), 63-74.
19. J. E. Goodman and R. Pollack, Allowable sequences and order types in discrete and computational geometry, in: New Trends in Discrete and Computational Geometry (J. Pach, ed.), Springer-Verlag, 1993, pp. 103-134.
20. B. Grünbaum, Arrangements of hyperplanes, Congr. Numer., 3 (1971), 41-106.
21. B. Grünbaum, Arrangements and Spreads, American Mathematical Society, Providence, RI, 1972.
22. S. Har-Peled, Constructing cuttings in theory and practice, SIAM J. Comput. 29 (2000), 2016-2039.
23. S. Har-Peled and M. Sharir, On-line point location in planar arrangements and its applications, Discrete Comput. Geom. 26 (2001), 19-40.
24. F. Levi, Die Teilung der projektiven Ebene durch Gerade oder Pseudogerade, Ber. Math.-Phys. Kl. sächs. Akad. Wiss. Leipzig, 78 (1926), 256-267.
25. J. Matousek, Reporting points in halfspaces, Comput. Geom. Theory Appl., 2 (1992), 169-186.
26. K. Mehlhorn, Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry, Springer-Verlag, Heidelberg, Germany, 1984.
27. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, New York, NY, 1995.
28. M. Sharir and S. Smorodinsky, On generalized geometric graphs and pseudolines, manuscript, 2001.
29. A. Solan, Cutting cycles of rods in space, Proc. 14th Annual Sympos. Comput. Geom., 1998, 135-142.
30. H. Tamaki and T. Tokuyama, How to cut pseudo-parabolas into segments, Discrete Comput. Geom., 19 (1998), 265-290.