Crown structures for vertex cover kernelization

Theory of Computing Systems

Volumn 41, Issue 3, 2007, Pages 411-430

  Abu Khzam, Faisal N ^a   Fellows, Michael R ^b   Langston, Michael A ^c   Suters, W Henry ^d  

^a LEBANESE AMERICAN UNIVERSITY   (Lebanon)

^b UNIVERSITY OF NEWCASTLE   (Australia)

^c University of Tennessee   (United States)

^d Carson Newman College   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY GRAPHS; CROWN STRUCTURE; KERNELIZATION; LOGICAL CONNECTIONS; POLYNOMIAL-TIME; SUBGRAPHS; VERTEX COVER; VERTEX COVER PROBLEMS;

LINEAR PROGRAMMING; POLYNOMIAL APPROXIMATION;

ALGORITHMS;

EID: 36849044049     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-007-1328-0     Document Type: Conference Paper

References (25)

1. F. N. Abu-Khzam. Topics in Graph Algorithms: Structural Results and Algorithmic Techniques, with Applications. Ph.D. thesis, Department of Computer Science, University of Tennessee, 2003.
2. F. N. Abu-Khzam, J. Cheetham, F. Dehne, M. A. Langston, S. Pitre, A. Rau-Chaplin, P. Shanbhag, and P. J. Taillon. ClustalXP, An extended and Parallel version of Chutea. See http://www.scs.carleton.ca/~dehne/proj/ clustalxp/bottom.htm.
3. F. N. Abu-Khzam, R. L. Collins, M. R. Fellows, M. A. Langston, W H. Suters, and C. T. Symons. Kernelization algorithms for the vertex cover problem: theory and experiments. In Proceedings, Workshop on Algorithm Engineering and Experiments (ALENEX), pages 62-69, 2004.
4. F. N. Abu-Khzam, M. A. Langston, P. Shanbhag, and C. T. Symons. Scalable parallel algorithms for FPT problems. Algorithmica, 45:269-286, 2006.
5. N. E. Baldwin, E. J. Chesler, S. Kirov, M. A. Langston, J. R. Snoddy, R. W Williams, and B. Zhang. Computational, integrative and comparative methods for the elucidation of genetic co-expression networks. Journal of Biomedicine and Biotechnology, 2:172-180, 2004.
6. J. F. Buss and J. Goldsmith. Nondeterminism within P. SIAM Journal on Computing, 22:560-572, 1993.
7. J. Cheetham, F. Dehne, A. Rau-Chaplin, U. Stege, and P. J. Taillon. Solving large FPT problems on coarse grained parallel machines. Journal of Computer and System Sciences, 67:691-706, 2003.
8. J. Chen, I. A. Kanj, and G. Xia. Simplicity Is Beauty: Improved Upper Bounds for Vertex Cover. Technical report, Texas A&M University, 2005.
9. E. J. Chesler and M. A. Langston. Combinatorial genetic regulatory network analysis tools for high throughput transcriptomic data. In Proceedings, First Annual RECOMB Satellite Workshop on Systems Biology and Second Annual RECOMB Satellite Workshop on Regulatory Genomics, pages 150-165, 2005.
10. E. J. Chesler, L. Lu, S. Shou, Y. Qu, J. Gu, J. Wang, H. C. Hsu, J. D. Mountz, N. E. Baldwin, M. A. Langston, J. B. Hogenesch, D. W Threadgill, K. F. Manly, and R. W. Williams. Complex trait analysis of gene expression uncovers polygenic and pleiotropic networks that modulate nervous system function. Nature Genetics, 37:233-242, 2005.
11. M. Chlebík and J. Chlebiková. Crown reductions for the minimum weighted vertex cover problem. Electronic Colloquium on Computational Complexity, Report No. 101, 2004.
12. 2) steps. In Proceedings, International Workshop on Graph Theoretic Concepts in ComputerScience, pages 257-269, 2004.
13. Vasek Chv'tal. Linear Programming. Freeman, New York, 1983.
14. OustalW. See http://helix.nih.gov/apps/bioinfo/clustalw.html.
15. W Cook. Private communication, 2003.
16. E. A. Dinic. Algorithm for solution of a problem of maximum flows in networks with power estimation. Soviet Mathematics Doklady, 11:1277-1280, 1970.
17. R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer-Verlag, New York, 1999.
18. M. R. Fellows and M. A. Langston. Nonconstructive tools for proving polynomial-time decidability. Journal of the ACM, 35:727-739, 1988.
19. M. R. Fellows and M. A. Langston. On search, decision and the efficiency of polynomial-time algorithms. Journal of Computer and Systems Sciences, 49:769-779, 1994.
20. D. Hochbaum. Approximation Algorithms for NP-hard Problems. PWS, Boston, MA, 1997.
21. S. Khuller. The vertex cover problem. ACM SIGACTNews, 33:31-33, June 2002.
22. NCBI. See http://www.ncbi.nlm.nih.gov/.
23. G.L. Nemhauser and L. E. Trotter. Vertex packings: structural properties and algorithms. Mathematical Programming, 8:232-248, 1975.
24. C. Sloper. Techniques in Parameterized Algorithm Design. Ph.D. thesis, Department of Computer Science, University of Bergen, Norway, 2005.
25. W H. Suters. Crown Decomposition: Theoretical Results and Practical Methods. Master's thesis, Department of Computer Science, University of Tennessee, 2004.