Improved algorithms and complexity results for power domination in graphs

Algorithmica (New York)

Volumn 52, Issue 2, 2008, Pages 177-202

  Guo, Jiong ^a   Niedermeier, Rolf ^a   Raible, Daniel ^b  

^a FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^b UNIVERSITY OF TRIER   (Germany)

Author keywords

(Power) domination in graphs; Computational complexity; Design and analysis of algorithms; Fixed parameter algorithms; Graph algorithms; Graphs of bounded treewidth; Parameterized complexity

Indexed keywords

(POWER) DOMINATION IN GRAPHS; ALGORITHMS AND COMPLEXITY; COMPUTATIONAL COMPLEXITY; DESIGN AND ANALYSIS OF ALGORITHMS; DOMINATING SETS; DOMINATION IN GRAPHS; DYNAMIC PROGRAMS; ELECTRIC POWER NETWORKS; FIXED-PARAMETER ALGORITHMS; GRAPH ALGORITHMS; GRAPHS OF BOUNDED TREEWIDTH; IN TREES; LINEAR-TIME ALGORITHMS; NP-COMPLETE; NP-COMPLETENESS; PARAMETERIZED; PARAMETERIZED COMPLEXITY; PLANAR GRAPHS; POWER DOMINATING SET; SPLIT GRAPHS; TREE-WIDTH; UNDIRECTED GRAPHS;

CHLORINE COMPOUNDS; CLUSTERING ALGORITHMS; ELECTRIC POWER SYSTEMS; GRAPH THEORY; NUCLEAR PROPULSION; TREES (MATHEMATICS);

SET THEORY;

EID: 50849142931     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-007-9147-x     Document Type: Article

References (35)

1. Aazami, A., Stilp, M.D.: Approximation algorithms and hardness for domination with propagation. In: Proc. 10th APPROX/11th RANDOM. Lecture Notes in Computer Science, vol. 4627, pp. 1-15. Springer, Berlin (2007)
2. Adjih, C., Jacquet, P., Viennot, L.: Computing connected dominating sets with multipoint relays. Ad Hoc Sens. Wirel. Netw. 1(1-2), 27-39 (2005)
3. Alber, J., Bodlaender, H.L., Fernau, H., Kloks, T., Niedermeier, R.: Fixed parameter algorithms for Dominating Set and related problems on planar graphs. Algorithmica 33(4), 461-493 (2002)
4. Alber, J., Fan, H., Fellows, M.R., Fernau, H., Niedermeier, R., Rosamond, F., Stege, U.: A refined search tree technique for Dominating Set on planar graphs. J. Comput. Syst. Sci. 71(4), 385-405 (2005)
5. Alber, J., Fellows, M.R., Niedermeier, R.: Polynomial time data reduction for Dominating Set. J. ACM 51(3), 363-384 (2004)
6. Alber, J., Niedermeier, R.: Improved tree decomposition based algorithms for domination-like problems. In: Proc. 5th LATIN. Lecture Notes in Computer Science, vol. 2286, pp. 613-628. Springer, Berlin (2002)
7. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation-Combinatorial Optimization Problems and Their Approximability Properties. Springer, Berlin (1999)
8. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci. 209, 1-45 (1998)
9. Bodlaender, H.L.: Treewidth: Characterizations, applications, and computations. In: Proc. 32nd WG. Lecture Notes in Computer Science, vol. 4271, pp. 1-14. Springer, Berlin (2006)
10. Booth, K.S., Johnson, J.H.: Dominating sets in chordal graphs. SIAM J. Comput. 11, 191-199 (1982)
11. Brandstädt, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications (1999)
12. Brueni, D.J., Heath, L.S.: The PMU placement problem. SIAM J. Discrete Math. 19(3), 744-761 (2005)
13. Demaine, E.D., Hajiaghayi, M.: Bidimensionality: New connections between FPT algorithms and PTASs. In: Proc. 16th SODA, pp. 590-601. ACM/SIAM, New York (2005)
14. Dewdney, A.K.: Fast Turing reductions between problems in NP: chap. 4; reductions between NP-complete problems. Technical report, Department of Computer Science, University of Western Ontario, Canada, 1981
15. Dorfling, M., Henning, M.A.: A note on power domination in grid graphs. Discrete Appl. Math. 154(6), 1023-1027 (2006)
16. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Berlin (1999)
17. Feige, U.: A threshold of ln∈n for approximating Set Cover. J. ACM 45(4), 634-652 (1998)
18. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006)
19. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
20. Guo, J., Hüffner, F., Niedermeier, R.: A structural view on parameterizing problems: distance from triviality. In: Proc. 1st IWPEC. Lecture Notes in Computer Science, vol. 3162, pp. 162-173. Springer, Berlin (2004)
21. Haynes, T.W., Hedetniemi, S.M., Hedetniemi, S.T., Henning, M.A.: Domination in graphs: applied to electric power networks. SIAM J. Discrete Math. 15(4), 519-529 (2002)
22. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Domination in Graphs: Advanced Topics. Pure and Applied Mathematics, vol. 209. Dekker, New York (1998)
23. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs, Pure and Applied Mathematics, vol. 208. Dekker, New York (1998)
24. Haynes, T.W., Henning, M.A.: Domination in graphs. In: Gross, J.L., Yellen, J. (eds.) Handbook of Graph Theory, pp. 889-909. CRC Press, Boca Raton (2004)
25. Keil, J.M.: The complexity of domination problems in circle graphs. Discrete Appl. Math. 36, 25-34 (1992)
26. Kloks, T.: Treewidth: Computations and Approximations. Lecture Notes in Computer Science, vol. 842. Springer, Berlin (1994)
27. Kneis, J., Mölle, D., Richter, S., Rossmanith, P.: Parameterized power domination complexity. Inf. Process. Lett. 98(4), 145-149 (2006)
28. Kratsch, D.: Algorithms. In: Haynes, T.W., Hedetniemi, S.T., Slater, P.J. (eds.) Domination in Graphs: Advanced Topics, pp. 191-231. Dekker, New York (1998)
29. Liao, C.S., Lee, D.T.: Power dominating problem in graphs. In: Proc. 11th COCOON. Lecture Notes in Computer Science, vol. 3595, pp. 818-828. Springer, Berlin (2005)
30. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, London (2006)
31. Raible, D.: Algorithms and complexity results for power domination in networks. Master's thesis, Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Germany (2005). (In German)
32. Reed, B.A.: Algorithmic aspects of tree width. In: Reed, B.A., Sales, C.L. (eds.) Recent Advances in Algorithms and Combinatorics, pp. 85-107. Springer, Berlin (2003)
33. Telle, J.A., Proskurowski, A.: Practical algorithms on partial k-trees with an application to domination-like problems. In: Proc. 3rd WADS. Lecture Notes in Computer Science, vol. 709, pp. 610-621. Springer, Berlin (1993)
34. Telle, J.A., Proskurowski, A.: Algorithms for vertex partitioning problems on partial k-trees. SIAM J. Discrete Math. 10(4), 529-550 (1997)
35. Vazirani, V.V.: Approximation Algorithms. Springer, Berlin (2001)