A (4+ε)-approximation for the minimum-weight dominating set problem in unit disk graphs

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

Volumn 5893 LNCS, Issue , 2009, Pages 135-146

  Erlebach, Thomas ^a   Mihalák, Matúš ^b  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION RATIOS; CONNECTED DOMINATING SET; CONSTANT FACTOR APPROXIMATION; DOMINATING SET PROBLEMS; DOMINATING SETS; FEASIBLE SOLUTION; STEINER TREES; UNIT DISK GRAPHS;

DISKS (STRUCTURAL COMPONENTS); TREES (MATHEMATICS);

APPROXIMATION ALGORITHMS;

EID: 78651241521     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-12450-1_13     Document Type: Conference Paper

References (18)

1. 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.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, pp. 3-14. Springer, Heidelberg (2006)
2. Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. J. ACM 41(1), 153-180 (1994)
3. Cheng, X., Huang, X., Li, D., Wu, W., Du., D.-Z.: A polynomial-time approximation scheme for the minimum-connected dominating set in ad hoc wireless networks. Networks 42(4), 202-208 (2003)
4. Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Math. 86(1-3), 165-177 (1990)
5. Dai, D., Yu, C.: A 5+ε-approximation algorithm for minimum weighted dominating set in unit disk graph. Theoret. Comput. Sci. 410(8-10), 756-765 (2009)
6. Feige, U.: A threshold of ln n for approximating set cover. J. ACM 45(4), 634-652 (1998)
7. Garey, M.R., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)
8. Guha, S., Khuller, S.: Improved methods for approximating node weighted Steiner trees and connected dominating sets. Inform. and Comput. 150(1), 57-74 (1999)
9. Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM 32(1), 130-136 (1985)
10. Huang, Y., Gao, X., Zhang, Z., Wu, W.: A better constant-factor approximation for weighted dominating set in unit disk graph. J. Comb. Optim. (2008)
11. Hunt III, H.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)
12. Lichtenstein, D.: Planar formulae and their uses. SIAM J. Comput. 11(2), 329-343 (1982)
13. Marathe, M.V., Breu, H., Hunt III, H.B., Ravi, S.S., Rosenkrantz, D.J.: Simple heuristics for unit disk graphs. Networks 25(2), 59-68 (1995)
14. Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: Proc. 11th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 770-779 (2000)
15. van Leeuwen, E.J.: Approximation algorithms for unit disk graphs. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 351-361. Springer, Heidelberg (2005)
16. Vazirani, V.V.: Approximation Algorithms. Springer, Heidelberg (2001)
17. Zou, F., Li, X., Gao, S., Wu, W.: Node-weighted Steiner tree approximation in unit disk graphs. Theoret. Comput. Sci. 18(4), 342-349 (2009)
18. Zou, F., Wang, Y., Xu, X.-H., Li, X., Du, H., Wan, P., Wu, W.: New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs. Theoret. Comput. Sci (2009) (Article in Press)