Approximating geometric coverage problems

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2008, Pages 1267-1276

  Erlebach, Thomas ^a   Van Leeuwen, Erik Jan ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b CWI   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DISKS (MACHINE COMPONENTS); DISKS (STRUCTURAL COMPONENTS); POLYNOMIAL APPROXIMATION; WIRELESS NETWORKS;

APPROXIMABILITY; COVERAGE PROBLEMS; DISK MODEL; NP-HARD; SET COVER; UNIT SQUARES;

APPROXIMATION ALGORITHMS;

EID: 58449108333     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. Arnbühl, C., Erlebach, T., Mihalák, M., Nunkesser, M., "Constant-Factor Approximation for Minimum- Weight (Connected) Dominating Sets in Unit Disk Graphs" in Proc. APPROX-RANDOM 2006, LNCS 4110, Springer-Verlag, Berlin, 2006, pp. 3-14.
2. Brönnimann, H., Goodrich, M.T., "Almost Optimal Set Covers in Finite VC-Dimension", Discrete Comput. Geom. 14 4 (1995), pp. 463-479.
3. Carmi, P., Katz, M.J., Lev-Tov, N., "Covering Points by Unit Disks of Fixed Location" in Proc. ISAAC 2007, LNCS, Springer, 2007. To appear.
4. Chan, T.M., "Polynomial-time approximation schemes for packing and piercing fat objects", J. Algorithms, 46 (2003), pp. 178-189.
5. Clark, B.N., Colbourn, C.J., Johnson, D.S., "Unit Disk Graphs", Discrete Math. 86 1-3 (1990), pp. 165-177.
6. Clarkson, K.L., Varadarajan, K.R., "Improved Approximation Algorithms for Geometric Set Cover", Discrete Comput. Geom. 37 1 (2007), pp. 43-58.
7. Demaine, E.D., Hajiaghaji, M.T., Feige, U., Salavatipour, M.R., "Combination Can Be Hard: Approximability of the Unique Coverage Problem" in Proc. SODA '06, ACM Press, New York, pp. 162-171.
8. Efrat, A.. Sharir, M., "The Complexity of the Union of Fat, Objects in the Plane", Discrete Comput. Geom. 23 2 (Feb. 2000), pp. 171-189.
9. Erlebach, T., Jansen, K., Seidel, E., "Polynomial-time Approximation Schemes for Geometric Intersection Graphs", SIAM J. Comput. 34 6 (2005), pp. 1302-1323.
10. Erlebach, T., van Leeuwen, E.J., "Domination in Geometric Intersection Graphs", Manuscript, 2007
11. Garey, M.R., Johnson, D.S., Computers and intractability - A Guide to the Theory of NP- Completeness, W.H. Freeman and Company, San Francisco, 1979.
12. Glaßer, C., Reith, S., Vollmer, H., "The Complexity of Base Station Positioning in Cellular Networks", Discrete Appl. Math. 148 1 (2005), pp. 1-12.
13. Guruswami, V., Trevisan, L., "The Complexity of Making Unique Choices: Approximating 1-in-k SAT" in Proc. APPROX-RANDOM 2005, LNCS 3624, Springer-Verlag, Berlin, 2005, pp. 99-110.
14. Hochbaum, D.S., Maass, W., "Approximation Schemes for Covering and Packing Problems in Image Processing and VLSI", J. ACM 32 1 (1985), pp. 130-136.
15. Khuller, S., Moss, A., Naor, J., "The Budgeted Maximum Coverage Problem", Inform. Process. Lett. 701 (April 1999), pp. 39-45.
16. Kuhn, F., von Rickenbach, P., Wattenhofer, R., Welzl, E., Zollinger, A., "Interference in Cellular Networks: The Minimum Membership Set Cover Problem" in Proc. COCOON 2005, LNCS 3595, Springer-Verlag, Berlin, 2005, pp. 188-198.
17. Lev-Tov, N., Peleg, D., "Exact Algorithms and Approximation Schemes for Base Station Placement, Problems" in Proc. SWAT 2002, LNCS 2368, Springer- Verlag, Berlin, 2002, pp. 90-99.
18. Moser, H., Raman, V., Sikdar, S., "The Parameterized Complexity of the Unique Coverage Problem" in Proc. ISAAC 2007, LNCS, Springer, 2007. To appear.
19. van Leeuwen, E.J., "Better Approximation Schemes for Disk Graphs" in Proc. SWAT 2006, LNCS 4059, Springer-Verlag, Berlin, 2006, pp. 316-327.