Short cycles make W-hard problems hard: FPT algorithms for W-hard problems in graphs with no short cycles

Algorithmica (New York)

Volumn 52, Issue 2, 2008, Pages 203-225

  Raman, Venkatesh ^a   Saurabh, Saket ^a  

^a INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

Dominating set; Independent set; Parameterized complexity; Set cover; T vertex cover

Indexed keywords

BIPARTITE GRAPHS; DOMINATING SET; DOMINATING SETS; FPT ALGORITHMS; HARD PROBLEMS; INDEPENDENT SET; INDEPENDENT SETS; INDUCED SUBGRAPH; PARAMETERIZED; PARAMETERIZED COMPLEXITY; SET COVER; SHORT CYCLES; SUB GRAPHS; T-VERTEX COVER; TRACTABLE ALGORITHMS; TRIANGLE-FREE GRAPHS; VERTEX COVER;

APPROXIMATION ALGORITHMS; CHLORINE COMPOUNDS; PARAMETER ESTIMATION; POLYNOMIAL APPROXIMATION; SET THEORY; TRIANGULATION;

GRAPH THEORY;

EID: 50849134862     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-007-9148-9     Document Type: Article

References (24)

1. Alber, J., Fellows, M.R., Niedermeier, R.: Polynomial time data reduction for dominating set. J. ACM 51(3), 363-384 (2004)
2. 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, 385-405 (2005)
3. Alekseev, V.E.: On easy and hard hereditary classes of graphs with respect to the independent set problem. Discrete Appl. Math. 132(1-3), 17-26 (2003)
4. Alekseev, V.E., Korobitsyn, D.V., Lozin, V.V.: Boundary classes of graphs for the dominating set problem. Discrete Math. 285(1-3), 1-6 (2004)
5. Bläser, M.: Computing small partial coverings. Inf. Process. Lett. 85(6), 327-331 (2003)
6. Downey, R.G., Fellows, M.R.: Threshold dominating sets and an improved characterization of W[2]. Theor. Comput. Sci. 209(1-2), 123-140 (1998)
7. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Berlin (1999)
8. Downey, R.G., Fellows, M.R., Vardy, A., Whittle, G.: The parametrized complexity of some fundamental problems in coding theory. SIAM J. Comput. 29(2), 545-570 (1999)
9. Downey, R.G., Fellows, M.R., Raman, V.: The complexity of irredundant sets parameterized by size. Discrete Appl. Math. 100(3), 155-167 (2000)
10. Duh, R., Fürer, M.: Approximation of k-set cover by semi-local optimization. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC), pp. 256-264 (1997)
11. Edmonds, J.: Paths, trees and flowers. Can. J. Math. 17, 449-467 (1965)
12. Feige, U.: A threshold of ln∈n for approximating set cover. J. ACM 45(4), 634-652 (1998)
13. Fernau, H.: Parameterized algorithms: a graph-theoretic approach. Habilitationsschrift, Universität Tübingen, Tübingen, Germany (2005)
14. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006)
15. n ). In: Proceedings of the 2nd International Workshop on Parameterized and Exact Computation (IWPEC). Lecture Notes in Computer Science, vol. 4169, pp. 184-191. Springer, Berlin (2006)
16. Guo, J., Niedermeier, R., Wernicke, S.: Parameterized complexity of generalized vertex cover problems. In: Proceeding of the 9th International Workshop Algorithms and Data Structures (WADS). Lecture Notes in Computer Science, vol. 3608, pp. 36-48. Springer, Berlin (2005)
17. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9(3), 256-278 (1974)
18. Jukna, S.: Extremal Combinatorics. Springer, Berlin (2001)
19. Khot, S., Raman, V.: Parameterized complexity of finding subgraphs with hereditary properties. Theor. Comput. Sci. 289(2), 997-1008 (2002)
20. Kortsarz, G., Peleg, D.: On choosing a dense subgraph. In: Proceeding of the 34th Annual Symposium on Foundations of Computer Science (FOCS), pp. 692-701 (1993)
21. Lovàsz, L.: On the ratio of optimal fractional and integral covers. Discrete Math. 13, 383-390 (1975)
22. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and Its Applications. Oxford University Press, London (2006)
23. Raman, V., Saurabh, S.: Triangles, 4-cycles and parameterized (in-)tractability. In: Proceeding of the 10th Scandinavian Workshop on Algorithm Theory (SWAT). Lecture Notes in Computer Science, vol. 4059, pp. 304-315. Springer, Berlin (2006)
24. Vazirani, V.V.: Approximation Algorithms. Springer, Berlin (2001)