Fixed parameter algorithms for DOMINATING SET and related problems on planar graphs

Algorithmica (New York)

Volumn 33, Issue 4, 2002, Pages 461-493

  Alber, J ^a   Bodlaender, H L ^b   Fernau, H ^a   Kloks, T ^c   Niedermeier, R ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

^b UTRECHT UNIVERSITY   (Netherlands)

^c NONE

Author keywords

FACE COVER; Fixed parameter tractability; NP complete problems; Outerplanarity; PLANAR DOMINATING SET; Planar graphs; Treewidth

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; PARAMETER ESTIMATION; POLYNOMIAL APPROXIMATION; SET THEORY; TREES (MATHEMATICS);

PLANAR GRAPHS;

COMPUTER SCIENCE;

EID: 0037507853     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00453-001-0116-5     Document Type: Article

References (47)

1. J. Alber, H. Fan, M. R. Fellows, H. Fernau, R. Niedermeier, F. Rosamond, and U. Stege. Refined search tree technique for DOMINATING SET on planar graphs. In Proceedings 26th MFCS 2001, pp. 111-122. LNCS 2136. Springer-Verlag, Berlin, 2001.
2. J. Alber, H. Fernau, and R. Niedermeier. Parameterized complexity: exponential speed-up for planar graph problems. In Proceedings 28th ICALP 2001, pp. 261-272. LNCS 2076. Springer-Verlag, Berlin, 2001. Long version available as Technical Report TR01-023, Electronic Colloquium on Computational Complexity (ECCC), Trier, March 2001.
3. J. Alber, H. Fernau, and R. Niedermeier. Graph separators: a parameterized view. In Proceedings 7th COCOON 2001, pp. 318-327. LNCS 2108. Springer-Verlag, Berlin, 2001. Long version available as Technical Report WSI-2001-8, Wilhelm-Schickard Institut für Informatik, Universität Tübingen.
4. J. Alber, J. Gramm, and R. Niedermeier. Faster exact solutions for hard problems: a parameterized point of view. Discrete Mathematics, 229:3-27, 2001.
5. J. Alber and R. Niedermeier. Improved tree decomposition based algorithms for domination-like problems. In Proceedings 5th LATIN 2002. LNCS, Springer-Verlag, April 2002.
6. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and the hardness of approximation problems. Journal of the ACM, 45:501-555, 1998.
7. B. Aspvall, A. Proskurowski, and J. A. Telle. Memory requirements for table computations in partial k-tree algorithms. Algorithmica, 27:382-394, 2000.
8. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi. Complexity and Approximation. Springer-Verlag, New York, 1999.
9. B. S. Baker. Approximation algorithms for NP-complete problems on planar graphs. Journal of the ACM, 41:153-180, 1994.
10. D. Bienstock and C. L. Monma. On the complexity of covering vertices by faces in a planar graph. SIAM Journal on Computing, 17:53-76, 1988.
11. H. L. Bodlaender. A linear time algorithm for finding tree-decompositions of small treewidth. SIAM Journal of Computing, 25:1305-1317, 1996.
12. H. L. Bodlaender. Treewidth: algorithmic techniques and results. In Proceedings 22nd MFCS '97, pp. 19-36. LNCS 1295. Springer-Verlag, Berlin, 1997.
13. H. L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science, 209:1-45, 1998.
14. A. Brandstädt, V. B. Le, and J. P. Spinrad. Graph Classes: A Survey. SIAM Monographs on Discrete Mathematics and Applications. Society for Industrial and Applied Mathematics, Philadelphia, PA, 1999.
15. L. Cai and D. Juedes. Subexponential parameterized algorithms collapse the W-hierarchy. In Proceedings 28th ICALP 2001, pp. 273-284. LNCS 2076. Springer-Verlag, Berlin, 2001. Flawed. Corrected in [16].
16. L. Cai and D. Juedes. On the existence of subexponential-time parameterized algorithms. Manuscript, November 2001.
17. J. Chen, I. Kanj, and W. Jia. Vertex cover: further observations and further improvements. Journal of Algorithms, 41:280-301, 2001.
18. P. Crescenzi and V. Kann. A compendium of NP optimization problems. Available at http://www.nada.kth.se/theory/problemlist.html, August 1998.
19. G. Di Battista, P. Eades, R. Tamassia, and I. G. Tollis. Graph Drawing; Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs, NJ, 1999.
20. R. Diestel. Graph Theory. Graduate Texts in Mathematics 173. Springer-Verlag, New York, 1997.
21. R. G. Downey and M. R. Fellows. Fixed-parameter tractability and completeness. Congressus Numerantium, 87:161-187, 1992.
22. R. G. Downey and M. R. Fellows. Parameterized computational feasibility. In P. Clote and J. Remmel (eds.) Feasible Mathematics II, pp. 219-244. Birkhauser, Boston, MA, 1995.
23. R. G. Downey and M. R. Fellows. Parameterized Complexity. Monographs in Computer Science. Springer-Verlag, New York, 1999.
24. R. G. Downey, M. R. Fellows, and U. Stege. Parameterized complexity: a framework for systematically confronting computational intractability, pp. 49-99. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 49. American Mathematical Society, Providence, RI, 1999.
25. U. Feige. A threshold of In n for approximating set cover. Journal of the ACM, 45:634-652, 1998.
26. M. R. Fellows. Parameterized complexity: new developments and research frontiers. In Aspects of Complexity (R. Downey, D. Hirschfeldt, eds.). De Gruyter, New York, 2001, pp. 51-72.
27. M. Frick and M. Grohe. Deciding first-order properties of locally tree-decomposable structures. In Proceedings 26th ICALP '99, pp. 331-340. LNCS 1644. Springer-Verlag, Berlin, 1999.
28. M. Garey and D. Johnson. Computers and Intractability: A Guide to the Theory of NP-CompIeteness. Freeman, San Francisco, CA, 1979.
29. M. M. Halldórsson, J. Kratochvíl, and J. A. Telle. Independent sets with domination constraints. In Proceedings 25th ICALP '98, pp. 176-187. LNCS 1443. Springer-Verlag, Berlin, 1998.
30. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater. Fundamentals of Domination in Graphs. Monographs and Textbooks in Pure and Applied Mathematics 208. Marcel Dekker, New York, 1998.
31. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater (eds.). Domination in Graphs; Advanced Topics. Monographs and Textbooks in Pure and Applied Mathematics 209. Marcel Dekker, New York, 1998.
32. D. S. Hochbaum (ed.). Approximation Algorithms for NP-Hard Problems. PWS, Boston, MA, 1997.
33. A. Kanevsky. Finding all minimum-size separating vertex sets in a graph. Networks, 23:533-541, 1993.
34. T. Kloks. Treewidth. Computations and Approximations. LNCS 842. Springer-Verlag, Berlin, 1994.
35. J. van Leeuwen. Graph Algorithms. In Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity, pp. 525-631. North-Holland, Amsterdam, 1990.
36. C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. Journal of the ACM, 41:960-981, 1994.
37. K. Mehlhorn. Graph Algorithms and NP-Completcness. Springer-Verlag, New York, 1984.
38. R. Niedermeier and P. Rossmanith. Upper bounds for Vertex Cover further improved. In Proceedings 16th STACS '99, pp. 561-570. LNCS 1563. Springer-Verlag, Berlin, 1999.
39. R. Niedermeier and P. Rossmanith. On efficient fixed parameter algorithms for Weighted Vertex Cover. In Proceedings 11th ISAAC 2000, pp. 180-191. LNCS 1969. Springer-Verlag, Berlin, 2000.
40. T. Nishizeki and N. Chiba. Planar Graphs: Theory and Applications. Annals of Discrete Mathematics 32. North-Holland, Amsterdam, 1988.
41. C. H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. Journal of Computer and System Sciences, 43:425-440, 1991.
42. C. H. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, MA, 1994.
43. A. Paz and S. Moran. Nondeterministic polynomial optimization problems and their approximations. Theoretical Computer Science, 15:251-277, 1981.
44. R. C. Read. Prospects for graph theory algorithms. Annals of Discrete Mathematics, 55:201-210, 1993.
45. J. A. Telle. Complexity of domination-type problems in graphs. Nordic Journal on Computing, 1:157-171, 1994.
46. J. A.Telle and A. Proskurowski. Practical algorithms on partial k-trees with an application to domination-like problems. In Proceedings 3rd WADS '93, pp. 610-621. LNCS 709. Springer-Verlag, Berlin, 1993.
47. J. A. Telle and A. Proskurowski. Algorithms for vertex partitioning problems on partial k-trees. SIAM Journal on Discrete Mathematics, 10(4):529-550, 1997.