The dominating set problem is fixed parameter tractable for graphs of bounded genus

Journal of Algorithms

Volumn 52, Issue 2, 2004, Pages 152-168

  Ellis, J ^b   Fan, H ^a   Fellows, M ^c  

^a WILFRID LAURIER UNIVERSITY   (Canada)

^b UNIVERSITY OF VICTORIA   (Canada)

^c UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Dominating set; Fixed parameter algorithm; Genus; Graph

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; GRAPH THEORY; LINEAR PROGRAMMING; PROBLEM SOLVING;

DOMINATING SET; FIXED PARAMETER ALGORITHMS; GENUS;

SET THEORY;

EID: 3042857277     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jalgor.2004.02.001     Document Type: Article

References (15)

1. Alber J., Bodlaender H.L., Fernau H., Niedermeier R. Fixed parameter algorithms for planar dominating set and related problems. Halldórsson M.M. 7th Scandinavian Workshop on Algorithm Theory. Lecture Notes in Comput. Sci. vol. 1851:2000;97-110.
2. Alber J., Fan H., Fellows M.R., Fernau H., Niedermeier R., Rosamond F., Stege U. Refined search tree techniques for the PLANAR DOMINATING SET problem. Sgall J., Pultr A., Kolman P. Mathematical Foundations of Computer Science. Lecture Notes in Comput. Sci. vol. 2136:2001;111-122 Springer.
3. Alber J., Fellows M., Niedermeier R. Efficient data reduction for dominating set: a linear problem kernel for the planar case. 8th Scandinavian Workshop on Algorithm Theory. Lecture Notes in Comput. Sci. vol. 2368:2002;150-159 Springer.
4. Arnborg S., Proskurowski A. Linear time algorithms for NP-hard problems restricted to partial k -trees. Discrete Appl. Math. 23:1989.
5. Bodlaender Hans L. A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25:(6):1996;1305-1317.
6. Bollóbas B. Combinatorics. 1986;Cambridge University Press.
7. Downey R.G., Fellows M.R. Parameterized computational feasibility. Clote P., Remmel J. Feasible Mathematics II. 1995;219-244 Birkhäuser.
8. Downey R.G., Fellows M.R. Parameterized Complexity. 1999;Springer.
9. Ellis J., Fan H., Fellows M. The dominating set problem is fixed parameter tractable for graphs of bounded genus. 8th Scandinavian Workshop on Algorithm Theory. Lecture Notes in Comput. Sci. vol. 2368:2002;180-189 Springer.
10. Garey M.R., Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness. 1979;Freeman.
11. Mohar B. Embedding graphs in an arbitrary surface in linear time. Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, Philadelphia, PA. 1996;392-397 ACM Press, New York, NY, USA.
12. Robertson N., Seymour P.D. Graph minors VIII. J. Combin. Theory Ser. B. 48:(2):1990;227-254.
13. Thomassen C. The graph genus problem is NP-complete. J. Algorithms. 10:(4):1989;568-576.
14. Thomassen C. The Jordan-Schonfliess theorem and the classification of surfaces. Amer. Math. Monthly. 99:1992;116-130.
15. Thomassen C. Embeddings and minors. Graham R.L., Groschel M., Lovász L. Handbook of Combinatorics. vol. I:1995;MIT Press.