Domination in geometric intersection graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4957 LNCS, Issue , 2008, Pages 747-758

  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

APPROXIMATION ALGORITHMS; COMPUTATIONAL GEOMETRY; POLYNOMIALS; SET THEORY; ASPECT RATIO; GRAPH THEORY; INTERSECTIONS; POLYNOMIAL APPROXIMATION;

GEOMETRIC INTERSECTION; INTERSECTION GRAPHS; SET PROBLEM; APPROXIMABILITY; APX-HARDNESS; CONSTANT-FACTOR APPROXIMATION ALGORITHMS; DOMINATING SETS; FAT OBJECTS; INAPPROXIMABILITY; INDEPENDENT SETS; INFORMATICS; LATIN AMERICAN; POLYNOMIAL-TIME APPROXIMATION SCHEMES; REGULAR POLYGONS; VERTEX COVER PROBLEMS;

GRAPH THEORY; APPROXIMATION ALGORITHMS;

EID: 43049125481     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-78773-0_64     Document Type: Conference Paper

References (26)

1. Alimonti, P., Kann, V.: Some APX-completeness results for cubic graphs. Theoret. Comput. Sci. 237(1-2), 123-134 (2000)
2. Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs. In: Díaz, J., Jansen, K., Rolim, J.D., Zwick, U. (eds.) Proc. APPROX-RANDOM 2006. LNCS, vol. 4110, pp. 3-14. Springer-Verlag, Berlin/Heidelberg (2006)
3. Baker, B.S.: Approximation Algorithms for NP-Complete Problems on Planar Graphs. J. ACM 41(1), 153-180 (1994)
4. Bar-Yehuda, R., Even, S.: A Linear-Time Approximation Algorithm for the Weighted Vertex Cover Problem. J. Algorithms 2(2), 198-203 (1981)
5. Brönnimann, H., Goodrich, M.T.: Almost Optimal Set Covers in Finite VC-Dimension. Discrete Comput. Geometry 14(4), 463-479 (1995)
6. Chan, T.M.: Polynomial-time Approximation Schemes for Packing and Piercing Fat Objects. J. Algorithms 46(2), 178-189 (2003)
7. Chang, M.-S.: Efficient Algorithms for the Domination Problems on Interval and CircularArc Graphs. SIAM J. Comput. 27(6), 1671-1694 (1998)
8. Chlebík, M., Chlebíková, J.: Approximation Hardness of Dominating Set Problems. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 192-203. Springer-Verlag, Berlin/Heidelberg (2004)
9. Chlebík, M., Chlebíková, J.: The Complexity of Combinatorial Optimization Problems on d-Dimensional Boxes. SIAM J. Discrete Math. 21(1), 158-169 (2007)
10. Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit Disk Graphs. Discrete Math. 86(1-3), 165-177 (1990)
11. Clarkson, K.L., Varadarajan, K.R.: Improved Approximation Algorithms for Geometric Set Cover. Discrete Comput. Geometry 37(1), 43-58 (2007)
12. Efrat, A., Sharir, M.: The Complexity of the Union of Fat Objects in the Plane. Discrete Comput. Geometry 23(2), 171-189 (2000)
13. Erlebach, T., Jansen, K., Seidel, E.: Polynomial-time Approximation Schemes for Geometric Intersection Graphs. SIAM J. Comput. 34(6), 1302-1323 (2005)
14. Even, G., Rawitz, D., Sharar, S.: Hitting Sets when the VC-Dimension is Small, Inform. Process. Lett. 95(2), 358-362 (2005)
15. Feige, U.: A Threshold of In n for Approximating Set Cover. J. ACM 45(4), 634-652 (1998)
16. Hochbaum, D.S.: Approximation Algorithms for the Set Covering and Vertex Cover Problems. SIAM J. Comput. 11(3), 555-556 (1982)
17. Hochbaum, D.S., Maass, W.: Approximation Schemes for Covering and Packing Problems in Image Processing and VLSI. J. ACM 32(1), 130-136 (1985)
18. Hunt III, D.B., Marathe, M.V., Radhakrishnan, V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E.: NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs. J. Algorithms 26(2), 238-274 (1998)
19. Kedem, K., Livne, R., Pach, J., Sharir, M.: On the Union of Jordan Regions and Collision-Free Translational Motion Amidst Polygonal Obstacles. Discrete Comput. Geometry 1, 59-70 (1986)
20. Kim, S.-J., Kostochka, A., Nakprasit, K.: On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane. Electr. J. Combinatorics 11, #R52 (2004)
21. Koebe, P.: Kontaktprobleme der konformen Abbildung. Ber. Ver. Sächs. Ak. Wiss. Leipzig, Math.-Phys. Kl, 88, 141-164 (1936)
22. Marathe, M.V., Breu, III, Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple Heuristics for Unit Disk Graphs. Networks 25, 59-68 (1995)
23. Marx, D.: Parameterized Complexity of Independence and Domination on Geometric Graphs. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 154-165. Springer-Verlag, Berlin/Heidelberg (2006)
24. Miller, G.L., Teng, S.-H., Thurston, W., Vavasis, S.A.: Separators for Sphere-Packings and Nearest Neighbor Graphs. J. ACM 44(1), 1-29 (1997)
25. Nieberg, T., Hurink, J.L.: A PTAS for the Minimum Dominating Set Problem, in Unit Disk Graphs. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 296-306. Springer-Verlag, Berlin/Heidelberg (2006)
26. van Leeuwen, E.J.: Better Approximation Schemes for Disk Graphs. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 316-327. Springer-Verlag, Berlin/Heidelberg (2006)