Vertex Cover: Further Observations and Further Improvements

Journal of Algorithms

Volumn 41, Issue 2, 2001, Pages 280-301

  Chen, Jianer ^a   Kanj, Iyad A ^b   Jia, Weijia ^c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b DEPAUL UNIVERSITY   (United States)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013072266     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.2001.1186     Document Type: Article

References (23)

1. R. Balasubramanian, M. R. Fellows, and V. Raman, An improved fixed parameter algorithm for vertex cover, Inform. Process. Lett. 65 (1998), 163-168.
2. R. Bar-Yehuda and S. Even, A local-ratio theorem for approximating the weighted vertex cover problem, Ann. Discrete Math. 25 (1985), 27-46.
3. R. Beigel, Finding maximum independent sets in sparse and general graphs, in "Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'99)," pp. 856-857, 1999.
4. n): a no-MIS algorithm, in "Proceedings of the 36th IEEE Symposium on Foundations of Computer Science (FOCS'95)," pp. 444-452, 1995.
5. J. F. Buss and J. Goldsmith, Nondeterminism within P, SIAM J. Comput. 22 (1993), 560-572.
6. J. Chen, I. A. Kanj, and W. Jia, Vertex cover: further observations and further improvements, in "Proceedings of the 25th International Workshop on Graph-Theoretical Concepts in Computer Science (WG'99)," Lecture Notes in Computer Science, Vol. 1665, pp. 313-324, Springer-Verlag, New York, 1999.
7. J. Chen, L. Liu, and W. Jia, Improvement on Vertex Cover for low-degree graphs, Networks 35 (2000), 253-259.
8. E. Dantsin, A. Goerdt, E. Hirsch, and U. Schöning, "Deterministic Algorithms for k-SAT Based on Covering Codes and Local Search," Lecture Notes in Computer Science, Vol. 1853, pp. 236-247, Springer-Verlag, New York, 2000.
9. R. G. Downey and M. R. Fellows, "Parameterized Complexity," Springer-Verlag, New York, 1999.
10. R. G. Downey and M. R. Fellows, Parameterized computational feasibility, in "Feasible Mathematics II" (P. Clote and J. Remmel, Eds.), pp. 219-244, Boston, Birkhauser, 1995.
11. R. G. Downey, M. R. Fellows, and U. Stege, Parameterized complexity: A framework for systematically confronting computational intractability, in "Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future" (F. Roberts, J. Kratochvil, and J. Nesetril, Eds.), AMS-DIMACS Proceedings Series, Vol. 49, pp. 49-99, Am. Math. Soc., Providence, 1999.
12. D. Hochbaum, Approximating covering and packing problems: Set cover, vertex cover, independent set, and related problems, in "Approximation Algorithms for NP-hard Problems" (D. Hochbaum, Ed.), pp. 94-143, PWS-Kent, Boston, 1997.
13. M. Garey and D. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness," Freeman, San Francisco, 1979.
14. 0.304n) algorithm for solving maximum independent set problem, IEEE Trans. Comput. 35 (1986), 847-851.
15. I. A. Kanj, "Vertex Cover: Exact and Approximate Algorithms and Applications," Ph.D. Dissertation, Department of Computer Science, Texas A&M University, 2001. [available from http://www.cs.tamu.edu/people/iakanj/research.html].
16. R. Niedermeier and P. Rossmanith, "Upper Bounds for Vertex Cover Further Improved," Lecture Notes in Computer Science, Vol. 1563, STACS'99, pp. 561-570, Springer-Verlag, New York, 1999.
17. R. Niedermeier and P. Rossmanith, A general method to speed up fixed-parameter-tractable algorithms, Inform. Process. Lett. 73 (2000), 125-129.
18. G. L. Nemhauser and L. E. Trotter, Vertex packing: structural properties and algorithms, Math. Programming 8 (1975), 232-248.
19. J. M. Robson, Algorithms for maximum independent sets, J. Algorithms 7 (1986), 425-440.
20. M. Shindo and E. Tomita, A simple algorithm for finding a maximum clique and its worst-case time complexity, Systems Comput. Japan 21 (1990), 1-13.
21. U. Schöning, A probabilistic approach for k-SAT and constraint satisfaction problems, in "Proceedings of the 40th IEEE Symposium on Foundations of Computer Science (FOCS'99)," pp. 410-414, 1999.
22. U. Stege and M. Fellows, An improved fixed-parameter-tractable algorithm for vertex cover, Technical Report 318, Department of Computer Science, ETH Zurich, April 1999.
23. R. E. Tarjan and A. E. Trojanowski, Finding a maximum independent set, SIAM J. Comput. 6 (1977), 537-546.