PTAS for geometric hitting set problems via local search

Proceedings of the Annual Symposium on Computational Geometry

Volumn , Issue , 2009, Pages 17-22

  Mustafa, Nabil H ^a   Ray, Saurabh ^b  

^a LAHORE UNIVERSITY OF MANAGEMENT SCIENCES   (Pakistan)

^b SAARLAND UNIVERSITY   (Germany)

Author keywords

Approximation algorithm; Epsilon nets; Hitting sets; Local search

Indexed keywords

ADMISSIBLE SET; FULLY POLYNOMIAL TIME APPROXIMATION; GEOMETRIC OBJECTS; HALF SPACES; HITTING SET PROBLEMS; HITTING SETS; LOCAL SEARCH; LOCAL SEARCH ALGORITHM; STRONGLY NP-HARD; UNIT DISK;

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; DISKS (MACHINE COMPONENTS); DISKS (STRUCTURAL COMPONENTS); LEARNING ALGORITHMS; POLYNOMIAL APPROXIMATION; RECURSIVE FUNCTIONS; SET THEORY;

APPROXIMATION ALGORITHMS;

EID: 70849098296     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1542362.1542367     Document Type: Conference Paper

References (18)

1. P. Agarwal and N. Mustafa. Independent set of intersection graphs of convex objects in 3d. Comput. Geom. Theory Appl., 34(2):83-95, 2006.
2. H. Bronnimann and M. Goodrich. Almost optimal set covers in finite VC-dimension. Discrete & Computational Geometry, 14(4):463- 479, 1995.
3. P. Carmi, M. Katz, and N. Lev-Tov. Covering points by unit disks of fixed location. In ISAAC, pages 644-655, 2007.
4. T. Chan and S. Har-Peled. Approximation algorithms for maximum independent set of pseudo-disks. In Proceedings of Symposium on Computational Geometry, 2009.
5. M. Chrobak and D. Eppstein. Planar orientations with low outdegree and compaction of adjacency matrices. Theor. Comput. Sci., 86(2):243-266, 1991.
6. K. Clarkson and K. Varadarajan. Improved approximation algorithms for geometric set cover. Discrete Comput. Geom., 37:43-58, 2007.
7. G. Even, D. Rawitz, and S. Shahar. Hitting sets when the VCdimension is small. Inf. Process. Lett., 95:358-362, 2005.
8. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, New York, NY, 1979.
9. D. Haussler and E. Welzl. Epsilon-nets and simplex range queries. Discrete Comput. Geom., 2:127-151, 1987.
10. D. S. Hochbaum and W. Maass. Fast approximation algorithms for a nonconvex covering problem. J. Algorithms, 8(3):305-323, 1987.
11. 1/6) time, parallel algorithm for solving planar laplacians. In Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pages 1002- 1011, 2007.
12. J. Matousek. Lectures in Discrete Geometry. Springer-Verlag, New York, NY, 2002.
13. J. Matousek, R. Seidel, and E. Welzl. How to net a lot with little: Small epsilon-nets for disks and halfspaces. In Proceedings of Symposium on Computational Geometry, pages 16-22, 1990.
14. S. Narayanappa and P. Vojtechovský. An improved approximation factor for the unit disk covering problem. In CCCG, 2006.
15. J. Pach and P. K. Agarwal. Combinatorial Geometry. John Wiley&Sons, New York, NY, 1995.
16. J. Pach and G. Woeginger. Some new bounds for epsilon-nets. In Symposium on Computational Geometry, pages 10-15, 1990.
17. E. Pyrga and S. Ray. New existence proofs for epsilon-nets. In Proceedings of Symposium on Computational Geometry, pages 199-207, 2008.
18. R. Raz and M. Safra. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In Proceedings of STOC, pages 475-484, 1997.