A fixed-parameter algorithm for the directed feedback vertex set problem

Journal of the ACM

Volumn 55, Issue 5, 2008, Pages

  Chen, Jianer ^a   Liu, Yang ^a   Lu, Songjian ^a   O'Sullivan, Barry ^b   Razgon, Igor ^b  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Deadlock; Feedback vertex set; Parameterized computation

Indexed keywords

ALGORITHMIC TECHNIQUES; DEADLOCK; DIRECTED GRAPHS; FEEDBACK VERTEX SET; FEEDBACK VERTEX SETS; FIXED-PARAMETER ALGORITHMS; OPEN PROBLEMS; PARAMETERIZED; PARAMETERIZED COMPUTATION; PARAMETERIZED COMPUTATIONS; RUNNING TIMES;

GRAPH THEORY;

PROBLEM SOLVING;

EID: 56349086571     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1411509.1411511     Document Type: Article

References (24)

1. BAFNA, V., BERMAN, P., AND FUJITO, T. 1999. A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. Disc. Math. 12, 289-297.
2. BODLAENDER, H. 1993. On linear time minor tests with depth first search. J. Algorithms 14, 1-23.
3. BODLAENDER, H. 2007. A cubic kernel for feedback vertex set. In Proceedings of the 24th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2007), Lecture Notes in Computer Science, vol. 4393. Springer-Verlag, New York, 320-331.
4. BODLAENDER, H., AND PENNINKX, E. 2008. A linear kernel for planar feedback vertex set. In Proceedings of the 3rd International Workshop on Parameterized and Exact Computation (IWPEC 2008), Lecture Notes in Computer Science, vol. 5018. Springer-Verlag, New York, 160-171.
5. CHEN, J., FOMIN, F., LIU, Y., LU, S., AND VILLANGER, Y. 2007a. Improved algorithms for the feedback vertex set problems. In Proceedings of the 10th Workshop on Algorithms and Data Structures (WADS'07), Lecture Notes in Computer Science, vol. 4619. Springer-Verlag, New York, 422-433.
6. CHEN, J., KANJ, I., AND JIA, W. 2001. Vertex cover: further observations and further improvements. J. Algorithms 41, 280-301.
7. CHEN, J., LIU, Y., AND LU, S. 2007b. An improved parameterized algorithm for the minimum node multiway cut problem. In Proceedings of the 10th Workshop on Algorithms and Data Structures (WADS'07), Lecture Notes in Computer Science, vol. 4619. Springer-Verlag, New York, 495-506.
8. 3) FPT algorithm for the undirected feedback vertex set problem. Theory Comput. Syst. 41, 479-492.
9. DOWNEY, R., AND FELLOWS, M. 1992. Fixed parameter intractability. In Proceedings of the 7th Annual Structural Complexity Conference. IEEE Computer Society Press, Los Alamitos, CA, 36-49.
10. DOWNEY, R., AND FELLOWS, M. 1995. Fixed-parameter tractability and completeness I: Basic results. SIAM J. Comput. 24, 873-921.
11. DOWNEY, R., AND FELLOWS, M. 1999. Parameterized Complexity. Springer-Verlag, New York.
12. EVEN, G., NAOR, J., SCHIEBER, B., AND SUDAN, M. 1998. Approximating minimum feedback sets and multicuts in directed graphs. Algorithmica 20, 151-174.
13. GARDARIN, G., AND SPACCAPIETRA, S. 1976. Integrity of databases: A general lockout algorithm with deadlock avoidance. In Modeling in Data Base Management System, G, Nijsssen, Ed. North-Holland, Amsterdam, The Netherlands, 395-411.
14. GAREY, M., AND JOHNSON, D. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York.
15. GUO, J., GRAMM, J., HÜFFNER, F., NIEDERMEIER, R., AND WERNICKE, S. 2005. Improved fixed-parameter algorithms for two feedback set problems. In Proceedings of the 9th Workshop on Algorithms and Data Structures (WADS'05), Lecture Notes in Computer Science, vol. 3608. Springer-Verlag, New York, 158-168.
16. GUO, J., GRAMM, J., HÜFFNER, F., NIEDERMEIER, R., AND WERNICKE, S. 2006. Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization. J. Comput. Syst. Sci. 72, 1386-1396.
17. GUTIN, G., AND YEO, A. 2008. Some parameterized problems on digraphs. Comput. J. 51, 363-371.
18. KARP, R. 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations, R. Miller and J. Thatcher, Eds. Plenum Press, New York, 85-103.
19. LEIGHTON, T., AND RAO, S. 1999. An approximation max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. J. ACM 46, 787-832.
20. LEISERSON, C., AND SAXE, J. 1991. Retiming synchronous circuitry. Algorithmica 6, 5-35.
21. LICHTENSTEIN, O., AND PNUELI, A. 1985. Checking that finite state concurrent programs satisfy their linear specification. In Proceedings of the 12th ACM Symposium on Principles of Programming Languages. ACM, New York, 97-107.
22. REED, B., SMITH, K., AND VETTA, A. 2004. Finding odd cycle transversals. Oper. Res. Lett. 32, 299-301.
23. SCHRUVER, A. 2003. Combinatorial Optimization. Springer-Verlag, Berlin, Germany.
24. SILBERSCHATZ, A., AND GALVIN, P. 1994. Operating System Concepts, 4th ed. Addison Wesley, Reading, MA.