Some lower bounds on geometric separability problems

International Journal of Computational Geometry and Applications

Volumn 16, Issue 1, 2006, Pages 1-26

  Arkin, Esther M ^a   Hurtado, Ferran ^b   Mitchell, Joseph S B ^a   Seara, Carlos ^b   Skiena, Steven S ^a  

^a Stony Brook University   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Lower bounds; Maximum gap; Separation

Indexed keywords

EID: 33644539202     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195906001902     Document Type: Article

References (20)

1. A. Aggarwal, H. Booth, J. O'Rourke and S. Suri, Finding minimal convex nested polygons, Inform. Comput. 83 (1989) 98-110.
2. E. M. Arkin, F. Hurtado, J. S. B. Mitchell, C. Seara and S. S. Skiena, Some separability problems in the plane, in Proc. 16th European Workshop on Computational Geometry, 2000, pp. 51-54.
3. M. Ben-Or, Lower bounds for algebraic computation trees, in Proc. 15th Ann. Symp. Theory of Computing, 1983, pp. 80-86.
4. B. K. Bhathacharya, Circular separability of planar point sets, in Computational Morphology, ed. G. T. Toussaint (North Holland, 1988).
5. J.-D. Boissonnat, J. Czyzowicz, O. Devillers, J. Urrutia and M. Yvinec, Computing largest circles separating two sets of segments, Int. J. Comput. Geom. Appl. 10(1) (2000) 41-53.
6. O. Devillers, F. Hurtado, M. Mora and C. Seara, Separating several point sets in the plane, in Proc. 13th Canadian Conf. Computational Geometry, 2001, pp. 81-84.
7. H. Edelsbrunner and F. P. Preparata, Minimum polygonal separation, Inform. Comput. 77 (1988) 218-232.
8. S. Fekete, On the complexity of min-link red-blue separation, manuscript, 1992.
9. S. Fisk, Separating point sets by circles, and the recognition of digital disks, IEEE Trans. Patt. Anal. Mach. Intell. 8(4) (1986) 554-556.
10. R. Freimer, Investigations in geometric subdivisions: Linear shattering and cartographic map coloring, Ph.D. Thesis, Computer Science, Cornell University, 2000.
11. R. Freimer, J. S. B. Mitchell and C. D. Piatko, On the complexity of shattering using arrangements, in Proc. 2nd Canadian Conf. Computational Geometry, 1990, pp. 218-222.
12. P. Gómez, F. Hurtado, S. Ramaswami, V. Sacristán and G. Toussaint, Implicit convex polygons, J. Math. Model. Algorith. 1 (2002) 57-85.
13. M. E. Houle, Algorithms for weak and wide separation of sets, Discr. Appl. Math. 45 (1993) 139-159.
14. F. Hurtado, M. Noy, P. A. Ramos and C. Seara, Separating objects in the plane with wedges and strips, Discr. Appl. Math. 109 (2001) 109-138.
15. F. Hurtado, M. Mora, P. A. Ramos and C. Seara, Separability by two lines and by nearly straight polygonal chains, Discr. Appl. Math. 144(1-2) (2004) 110-122.
16. D. T. Lee and Y. F. Wu, Geometric complexity of some location problems, Algorithmic 1 (1986) 193-211.
17. 3 and related problems, SIAM J. Comput. 12(4) (1983) 759-776.
18. J. O'Rourke, S. R. Kosaraju and N. Megiddo, Computing circular separability, Discr. Comput. Geom. 1(1) (1986) 105-113.
19. P. Ramanan, Obtaining lower bounds using artificial components, Inform. Process. Lett. 24 (1987) 243-246.
20. D. P. Wang and R. C. T. Lee, An optimal algorithm for solving the restricted minimal convex nested polygonal separation problem, in Proc. 5th Canadian Conf. Computational Geometry, 1993, pp. 334-339.