Algorithms for generalized halfspace range searching and other intersection searching problems

Computational Geometry: Theory and Applications

Volumn 5, Issue 6, 1996, Pages 321-340

  Gupta, Prosenjit ^a   Janardan, Ravi ^a   Smid, Michiel ^b  

^a University of Minnesota   (United States)

^b MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Computational geometry; Data structures; Filtering search; Geometric duality; Intersection searching; Persistence

Indexed keywords

EID: 0041063641     PISSN: 09257721     EISSN: None     Source Type: Journal    
DOI: 10.1016/0925-7721(94)00019-0     Document Type: Article

References (23)

1. P.K. Agarwal and M. van Kreveld, Connected component and simple polygon intersection searching, in: Proceedings of the 3rd Workshop on Algorithms and Data Structures (1993) 36-47.
2. P.K. Agarwal, M. van Kreveld and M. Overmars, Intersection queries for curved objects, J. Algorithms 15 (1993) 229-266.
3. A. Aggarwal, M. Hansen and T. Leighton, Solving query-retrieval problems by compacting Voronoi diagrams, In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing (1990) 331-340.
4. B. Chazelle, Filtering search: a new approach to query-answering, SIAM J. Comput. 15 (1986) 703-724.
5. B. Chazelle, L.J. Guibas and D.T. Lee, The power of geometric duality, BIT 25 (1985) 76-90.
6. S.W. Cheng and R. Janardan, Algorithms for ray-shooting and intersection searching, J. Algorithms 13 (1992) 670-692.
7. P.F. Dietz and D.D. Sleator, Two algorithms for maintaining order in a list, in: Proceedings of the 19th Annual ACM Symposium on Theory of Computing (1987) 365-372.
8. D.P. Dobkin and H. Edelsbrunner, Space searching for intersecting objects, J. Algorithms 8 (1987) 348-361.
9. J.R. Driscoll, N. Sarnak, D.D. Sleator and R.E. Tarjan, Making data structures persistent, J. Comput. System Sci. 38 (1989) 86-124.
10. H. Edelsbrunner, Algorithms in Combinatorial Geometry (Springer, New York, 1987).
11. P. Gupta, R. Janardan and M. Smid, Efficient algorithms for generalized intersection searching on non-iso-oriented objects, Technical Report TR-93-73, Dept. of Computer Science, University of Minnesota, 1993.
12. P. Gupta, R. Janardan and M. Smid, Further results on generalized intersection searching problems: counting, reporting, and dynamization, J. Algorithms (1995); Preliminary version, in: Proceedings of the 3rd Workshop on Algorithms and Data Structures, Montréal, Canada (1993) 361-372.
13. P. Gupta, R. Janardan and M. Smid, Further results on generalized intersection searching problems: counting, reporting, and dynamization, J. Algorithms (1995); Preliminary version, in: Proceedings of the 3rd Workshop on Algorithms and Data Structures, Montréal, Canada (1993) 361-372.
14. P. Gupta, R. Janardan and M. Smid, On intersection searching problems involving curved objects, in: Proceedings of the 4th Scandinavian Workshop on Algorithm Theory, Aarhus, Denmark, LNCS Vol. 824 (1994) 183-194.
15. R. Janardan and M. Lopez, Generalized intersection searching problems, Interna. J. Comput. Geom. Appl. 3 (1993) 39-69.
16. J. Matoušek, Cutting hyperplane arrangements, Discrete Comput. Geom. 6 (1991) 385-406.
17. J. Matoušek, Efficient partition trees, Discrete Comput. Geom. 8 (1992) 315-334.
18. J. Matoušek, Range searching with efficient hierarchical cuttings, Discrete Comput. Geom. 10 (1992) 157-182.
19. J. Matoušek and O. Schwarzkopf, On ray shooting in convex polytopes, Discrete Comput. Geom. 10 (1993) 215-232.
20. M.H. Overmars and C.K. Yap, New upper bounds in Klee's measure problem, SIAM J. Comput. 20 (1991) 1034-1045.
21. M. Sharir, Davenport-schinzel sequences and their geometric applications, in: R. A. Earnshaw, ed., Theoretical Foundations of Computer Graphics and CAD (Springer, New York, 1988) 253-278.
22. M. van Kreveld, New results on data structures in computational geometry, Ph.D. Thesis, Department of Computer Science, University of Utrecht, Utrecht, Netherlands, 1992.
23. E. Welzl, More on k-sets of finite sets in the plane, Discrete Comput. Geom. 1 (1986) 95-100.