On the minimum feedback vertex set problem: Exact and enumeration algorithms

Algorithmica (New York)

Volumn 52, Issue 2, 2008, Pages 293-307

  Fomin, Fedor V ^a   Gaspers, Serge ^a   Pyatkin, Artem V ^b   Razgon, Igor ^c  

^a UNIVERSITY OF BERGEN   (Norway)

^b SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^c UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Exact exponential algorithm; Maximum induced forest; Minimum feedback vertex set; Number of minimal feedback vertex sets

Indexed keywords

ENUMERATION ALGORITHMS; EXACT EXPONENTIAL ALGORITHM; FEEDBACK VERTEX SETS; MAXIMUM INDUCED FOREST; MINIMUM FEEDBACK VERTEX SET; NUMBER OF MINIMAL FEEDBACK VERTEX SETS;

EID: 50849102034     PISSN: 01784617     EISSN: 14320541     Source Type: Journal    
DOI: 10.1007/s00453-007-9152-0     Document Type: Article

References (33)

1. Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Discrete Math. 12, 289-297 (1999)
2. Bar-Yehuda, R., Geiger, D., Naor, J., Roth, R.M.: Approximation algorithms for the feedback vertex set problem with applications to constraint satisfaction and Bayesian inference. SIAM J. Comput. 27, 942-959 (1998)
3. Björklund, A., Husfeldt, T.: Inclusion-exclusion algorithms for counting set partitions. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), pp. 575-582. IEEE Computer Society, Los Alamitos (2006)
4. Brunetta, L., Maffioli, F., Trubian, M.: Solving the feedback vertex set problem on undirected graphs. Discrete Appl. Math. 101, 37-51 (2000)
5. Byskov, J.M.: Enumerating maximal independent sets with applications to graph colouring. Oper. Res. Lett. 32, 547-556 (2004)
6. Byskov, J.M., Madsen, B.A., Skjernaa, B.: On the number of maximal bipartite subgraphs of a graph. J. Graph Theory 48, 127-132 (2005)
7. Cai, M.-C., Deng, X., Zang, W.: A min-max theorem on feedback vertex sets. Math. Oper. Res. 27, 361-371 (2002)
8. Chen, J., Liu, Y., Lu, S.: Directed feedback vertex set problem is FPT. Dagstuhl Seminar Series, Seminar 07281 (2007), available electronically at http://kathrin.dagstuhl.de/files/Materials/07/07281/07281.ChenJianer.Paper.pdf
9. Chudak, F.A., Goemans, M.X., Hochbaum, D.S., Williamson, D.P.: A primal-dual interpretation of two 2-approximation algorithms for the feedback vertex set problem in undirected graphs. Oper. Res. Lett. 22, 111-118 (1998)
10. 3) FPT algorithm for the undirected feedback vertex set problem. In: Proceedings of the 11th Annual International Conference on Computing and Combinatorics (COCOON 2005). Lecture Notes in Comput. Sci., vol. 3595, pp. 859-869. Springer, Berlin (2005)
11. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, New York (1999)
12. Even, G., Naor, J., Schieber, B., Zosin, L.: Approximating minimum subset feedback sets in undirected graphs with applications. SIAM J. Discrete Math. 13, 255-267 (2000)
13. Festa, P., Pardalos, P.M., Resende, M.G.C.: Feedback set problems. In: Handbook of Combinatorial Optimization, Supplement vol. A, pp. 209-258. Kluwer Academic, Dordrecht (1999)
14. Fomin, F.V., Pyatkin, A.V.: Finding minimum feedback vertex set in bipartite graph. Reports in Informatics 291, University of Bergen (2005)
15. Fomin, F.V., Grandoni, F., Kratsch, D.: Measure and conquer: domination-a case study. In: Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP 2005). Lecture Notes in Comput. Sci., vol. 3580, pp. 191-203. Springer, Berlin (2005)
16. Fomin, F.V., Grandoni, F., Kratsch, D.: Some new techniques in design and analysis of exact (exponential) algorithms. Bull. EATCS 87, 47-77 (2005)
17. Fomin, F.V., Grandoni, F., Pyatkin, A.V., Stepanov, A.: Bounding the number of minimal dominating sets: a measure and conquer approach. In: Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC 2005). Lecture Notes in Comput. Sci., vol. 3827, pp. 573-582. Springer, Berlin (2005)
18. n ). In: Proceedings of the 2nd International Workshop on Parameterized and Exact Computation (IWPEC 2006). Lecture Notes in Comput. Sci., vol. 4169, pp. 184-191. Springer, Berlin (2006)
19. 0.288∈n ) independent set algorithm. In: 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006), pp. 18-25. ACM and SIAM, New York (2006)
20. Funke, M., Reinelt, G.: A polyhedral approach to the feedback vertex set problem. In: Integer Programming and Combinatorial Optimization. Lecture Notes in Comput. Sci., vol. 1084, pp. 445-459. Springer, Berlin (1996)
21. Guo, J., Niedermeier, R., Wernicke, S.: Parameterized complexity of generalized vertex cover problems. In: Proceedings of the 9th International Workshop on Algorithms and Data Structures (WADS 2005). Lecture Notes in Comput. Sci., vol. 3608, pp. 36-48. Springer, Berlin (2005)
22. Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85-103. Plenum, New York (1972)
23. Kleinberg, J., Kumar, A.: Wavelength conversion in optical networks. J. Algorithms 38, 25-50 (2001)
24. n ) algorithm for graph coloring and other partitioning problems via inclusion-exclusion. In: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006), pp. 583-590. IEEE Computer Society, Los Alamitos (2006)
25. Moon, J.W., Moser, L.: On cliques in graphs. Isr. J. Math. 3, 23-28 (1965)
26. Pardalos, P.M., Qian, T., Resende, M.G.C.: A greedy randomized adaptive search procedure for the feedback vertex set problem. J. Comb. Optim. 2, 399-412 (1999)
27. Raman, V., Saurabh, S., Sikdar, S.: Improved exact exponential algorithms for vertex bipartization and other problems. In: Proceedings of the 9th Italian Conference on Theoretical Computer Science (ICTCS 2005). Lecture Notes in Comput. Sci., vol. 3701, pp. 375-389. Springer, Berlin (2005)
28. Raman, V., Saurabh, S., Subramanian, C.R.: Faster fixed parameter tractable algorithms for undirected feedback vertex set. In: Proceedings of the 13th International Symposium on Algorithms and Computation (ISAAC 2002). Lecture Notes in Comput. Sci., vol. 2518, pp. 241-248. Springer, Berlin (2002)
29. Razgon, I.: Exact computation of maximum induced forest. In: Proceedings of the 10th Scandinavian Workshop on Algorithm Theory (SWAT 2006). Lecture Notes in Comput. Sci., pp. 160-171. Springer, Berlin (2006)
30. Razgon, I.: Directed feedback vertex set is fixed-parameter tractable. Dagstuhl Seminar Series, Seminar 07281 (2007), available electronically at http://kathrin.dagstuhl.de/files/Submissions/07/07281/07281.RazgonIgor.Paper!. pdf
31. Robson, J.M.: Algorithms for maximum independent sets. J. Algorithms 7, 425-440 (1986)
32. Schwikowski, B., Speckenmeyer, E.: On enumerating all minimal solutions of feedback problems. Discrete Appl. Math. 117, 253-265 (2002)
33. Woeginger, G.: Exact algorithms for NP-hard problems: a survey. In: Combinatorial Optimization-Eureka, You Shrink!. Lecture Notes in Comput. Sci., vol. 2570, pp. 185-207. Springer, Berlin (2003)