Geometric packing under non-uniform constraints

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2012, Pages 11-20

  Ene, Alina ^a   Har Peled, Sariel ^a   Raichel, Benjamin ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Independent set; Optimization; Rounding scheme

Indexed keywords

HYPER GRAPH; INDEPENDENT SET; OPTIMAL SOLUTIONS; ROUNDING SCHEMES; WEIGHTED REGIONS;

OPTIMIZATION;

COMPUTATIONAL GEOMETRY;

EID: 84863960578     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2261250.2261253     Document Type: Conference Paper

References (27)

1. B. Aronov, M. de Berg, E. Ezra, and M. Sharir. Improved bound for the union complexity of locally fat objects in the plane. manuscript, 2011.
2. B. Aronov, M. de Berg, E. Ezra, and M. Sharir. Improved bound for the union of fat objects in the plane. manuscript, 2011.
3. B. Aronov, E. Ezra, and M. Sharir. Small-size ε-nets for axis-parallel rectangles and boxes. SIAM J. Comput., 39(7):3248-3282, 2010.
4. P. Cappanera. A survey on obnoxious facility location problems. Technical report, University of Pisa, 1999.
5. P. Chalermsook and J. Chuzhoy. Maximum independent set of rectangles. In Proc. 20th ACM-SIAM Sympos. Discrete Algorithms, pages 892-901, 2009.
6. T. M. Chan. Polynomial-time approximation schemes for packing and piercing fat objects. J. Algorithms, 46(2):178-189, 2003.
7. T. M. Chan and S. Har-Peled. Approximation algorithms for maximum independent set of pseudo-disks. In Proc. 25th Annu. ACM Sympos. Comput. Geom., pages 333-340, 2009. cs.uiuc.edu/~sariel/papers/08/w-indep.
8. T. M. Chan and S. Har-Peled. Approximation algorithms for maximum independent set of pseudo-disks. CoRR, abs/1103.1431, 2011.
9. C. Chekuri, K. L. Clarkson., and S. Har-Peled. On the set multi-cover problem in geometric settings. In Proc. 25th Annu. ACM Sympos. Comput. Geom., pages 341-350, 2009.
10. M. Chlebík and J. Chlebíková. The complexity of combinatorial optimization problems on d-dimensional boxes. SIAM J. Discrete Math., 21(1):158-169, 2007.
11. K. L. Clarkson. Applications of random sampling in computational geometry, II. In Proc. 4th Annu. ACM Sympos. Comput. Geom., pages 1-11, 1988.
12. K. L. Clarkson and P. W. Shor. Applications of random sampling in computational geometry, II. Discrete Comput. Geom., 4:387-421, 1989.
13. M. de Berg, O. Cheong, M. van Kreveld, and M. H. Overmars. Computational Geometry: Algorithms and Applications. Springer-Verlag, 3rd edition, 2008.
14. A. Ene, S. Har-Peled, and B. Raichel. Geometric packing under non-uniform constraints. CoRR, abs/1107.2949, 2011.
15. T. Erlebach, K. Jansen, and E. Seidel. Polynomial-time approximation schemes for geometric intersection graphs. SIAM J. Comput., 34(6):1302-1323, 2005.
16. E. Ezra, B. Aronov, and M. Sharir. Improved bound for the union of fat triangles. In Proc. 16th ACM-SIAM Sympos. Discrete Algorithms, pages 1778-1785, 2011.
17. J. Fox and J. Pach. Computing the independence number of intersection graphs. In Proc. 22nd ACM-SIAM Sympos. Discrete Algorithms, pages 1161-1165, 2011.
18. E. Grant and T. M. Chan. Exact algorithms and apx-hardness results for geometric set cover. In Proc. 23rd Canad. Conf. Comput. Geom., 2011.
19. S. Har-Peled. Being fat and friendly is not enough. CoRR, abs/0908.2369, 2009.
20. 1-ε. Acta Mathematica, pages 105-142, 1999.
21. V. Kann. Maximum bounded 3-dimensional matching is max snp-complete. Inform. Process. Lett., 37:27-35, January 1991.
22. N. H. Mustafa and S. Ray. Improved results on geometric hitting set problems. Discrete Comput. Geom., 44(4):883-895, 2010.
23. A. Srinivasan. New approaches to covering and packing problems. In Proc. 12th ACM-SIAM Sympos. Discrete Algorithms, pages 567-576, 2001.
24. P. G. Szabó, M. Cs. Markót, T. Csendes, E. Specht, L. G. Casado, and I. Garcãa. New Approaches to Circle Packing in a Square: With Program Codes (Springer Optimization and Its Applications). Springer-Verlag New York, Inc., 2007.
25. A. Tamir. Obnoxious facility location on graphs. SIAM J. Discrete Math., 4(4):550-567, 1991.
26. K. Varadarajan. Weighted geometric set cover via quasi-uniform sampling. In Proc. 42nd Annu. ACM Sympos. Theory Comput., pages 641-648, 2010.
27. D. P. Williamson and D. B. Shmoys. The Design of Approximation Algorithms. Cambridge University Press, 2011.