Computing the volume of the union of cubes

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2007, Pages 294-301

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

^a Duke University   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

Arrangements; Union of objects

Indexed keywords

AXIS-ALIGNED BOXES; UNION OF OBJECTS;

ALGORITHMS; NUMERICAL METHODS; SET THEORY;

COMPUTATION THEORY;

EID: 35348815511     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1247069.1247121     Document Type: Conference Paper

References (12)

1. http://en.wikipedia.org/wiki/Klee's-measure_problem
2. D. Attali and H. Edelsbrunner, Inclusion-exclusion formulas from independent complexes, Proc. 21st Ann. Sympos. Comput. Geom., 2005, 247-254.
3. M. de Berg, M. van Kreveld, M. Overmars and O. Schwarzkopf, Computational Geometry: Algorithms and Applications, 2nd edition, Springer Verlag, Heidelberg, 2000.
4. J. L. Bentley, Algorithms for Klee's rectangle problems. Unpublished notes, Computer Science Department, Carnegie Mellon University, 1977.
5. J.D. Boissonnat, M. Sharir, B. Tagansky and M. Yvinec, Voronoi diagrams in higher dimensions under certain polyhedral distance functions, Discrete Comput. Geom. 19 (1998), 485-519.
6. E. Chen and T. M. Chan, Space-efficient algorithms for Klee's measure problem, Proc. 17th Canadian Conf. Comput. Geom., 2005.
7. B. S. Chlebus, On the Klee's measure problem in small dimensions, Proc. 25th Conf. Current Trends in Theory and Practice of Informatics, 1998, 304-311.
8. H. Edelsbrunner, The union of balls and its dual shape, Discrete Comput. Geom. 13 (1995), 415-440.
9. i], Commun. ACM 21 (1978), 540-544.
10. J. van Leeuwen and D. Wood, The measure problem for rectangular ranges in d-space, J. Algorithms 2 (1981), 282-300.
11. i] be computed in less than O(n log n) steps? Amer. Math. Monthly 84 (1977), 284-285.
12. M. Overmars and C.K. Yap, New upper bounds in Klee's measure problem, SIAM J. Comput. 20 (1991), 1034-1045.