Efficient exact algorithms through enumerating maximal independent sets and other techniques

Theory of Computing Systems

Volumn 41, Issue 3, 2007, Pages 563-587

  Raman, Venkatesh ^a   Saurabh, Saket ^a   Sikdar, Somnath ^a  

^a INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EDGE DOMINATING SET; EFFICIENT EXACT ALGORITHMS; EXACT EXPONENTIAL-TIME ALGORITHMS; FEEDBACK VERTEX SET PROBLEMS; MAXIMAL INDEPENDENT SET; MINIMUM MAXIMAL MATCHING; ODD CYCLE TRANSVERSALS; PARAMETERIZED ALGORITHM;

COMPUTATIONAL COMPLEXITY;

ALGORITHMS;

EID: 36849093348     PISSN: 14324350     EISSN: 14330490     Source Type: Journal    
DOI: 10.1007/s00224-007-1334-2     Document Type: Conference Paper

References (42)

1. J. Alber, H. Fan, M. R. Fellows, H. Fernau, R. Niedermeier, F. Rosamond and U. Stege. A refined search tree technique for Dominating Set on planar graphs. Journal of Computer and System Sciences 71(4): 385-405 (2005).
2. A. Björklund and T. Husfeldt. Exact algorithms for exact satisfiability and number of perfect matchings. To appear in Proceedings of the 33rd International Colloquium on Automata, Languages and Programming (ICALP). Lecture Notes in Computer Science, Springer-Verlag, Berlin (2006).
3. J. M. Byskov. Exact Algorithms for Graph Colouring and Exact Satisfiability. Ph.D. dissertation (2004).
4. J. M. Byskov. Enumerating maximal independent sets with applications to graph colouring. Operations Research Letters 32(6): 547-556 (2004).
5. J. Chen. Parameterized computation and complexity: a new approach dealing with NP-hardness. Journal of Computer Science and Technology 20(1): 18-37 (2005).
6. J. Chen and I. A. Kanj. Constrained minimum vertex cover in bipartite graphs: complexity and param-eterized algorithms. Journal of Computer and System Sciences 67(4): 833-847 (2003).
7. R. Downey. Parameterized complexity for the skeptic. In Proceedings of the 18th IEEE Conference on Computational Complexity, pp. 147-169 (2003).
8. R. Downey and M. Fellows. Parameterized Complexity. Springer-Verlag, New York (1999).
9. D. Eppstein. Small maximal independent sets and faster exact graph coloring. In Proceedings of the 7th Workshop on Algorithms and Data Structures (WADS), pp. 462-470. Lecture Notes in Computer Science 2125. Springer-Verlag, Berlin (2001).
10. D. Eppstein. 3-coloring in time 0(1.3289"). Journal of Algorithms 54 (2): 168-204 (2005).
11. H. Fernau. Parameterized algorithmics for d-Hitting Set. Manuscript.
12. H. Fernau and R. Niedermeier. An efficient exact algorithm for constraint bipartite vertex cover. Journal of Algorithms 38(2): 374-410 (2001).
13. J. Flum and M. Grohe. Parameterized Complexity Theory. Springer EATCS Series, New York (2006).
14. n). Manuscript (2006).
15. R V. Fomin, R Grandoni and D. Kratsch. Some new techniques in design and analysis of exact (exponential) algorithms. Bulletin of the European Association for Theoretical Computer Science (EATCS) 87: 47-77 (2005).
16. R V. Fomin and A. V. Pyatkin. Finding Feedback Vertex Set in a Bipartite Graph. Report No. 291, Department of Informatics, University of Bergen (2005).
17. M. Fürer and S. P. Kasiviswanathan. Algorithms for counting 2-SAT solutions and colourings with applications. Electronic Colloquium on Computational Complexity (ECCC) 33 (2006).
18. R Gavril and M. Yannakakis. Edge dominating sets in graphs. SIAM Journal on Applied Mathematics 38(3): 364-372 (1980).
19. J. Gramm, J. Guo, R Hüffner and R. Niedermeier. Automated generation of search tree algorithms for hard graph modification, problems. Algorithmica 39(4): 321-347 (2004).
20. J. Gramm, E. A. Hirsch, R. Niedermeier and P. Rossmanith. Worst-case upper bounds for MAX-2-SAT with, an application to MAX-CUT. Discrete Applied Mathematics 130 (2): 139-155 (2003).
21. J. Guo, J. Gramm, R Hüffner, R. Neidermeier and S. Wernicke. Improved fixed-parameter algorithms for two feedback set problems. In Proceedings of the 9th Workshop on Algorithms and Data Structures (WADS), pp. 158-168. Lecture Notes in Computer Science 3608. Springer-Verlag, Berlin (2005).
22. M. Hujter and Z. Tuza. The number of maximal independent sets in triangle-free graphs. SIAM Journal on Discrete Mathematics 6(2): 284-288 (1993).
23. K. Iwama and S. Tamaki. Improved upper bounds for 3-SAT. In Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA): 328 (2004).
24. D. S. Johnson, M. Yannakakis and C. H. Papadimitriou. On generating all maximal independent sets. Information Processing Letters 27: 119-123 (1988).
25. E. L. Lawler. A note on the complexity of the chromatic number. Information Processing Letters 5(3): 66-67 (1976).
26. D. Lokshtanov and C. Sloper. Fixed parameter set splitting, linear kernel and improved running time. In Proceedings of Algorithms and Complexity in Durham (ACID), pp. 105-113 (2005).
27. D. Mölle, S. Richter and P. Rossmanith. A faster algorithm for the Steiner tree problem. In Proceedings of the 23rd Symposium on Theoretical Aspects of Computer Science, pp. 561-570. Lecture Notes in Computer Science 3884. Springer-Verlag, Berlin (2006).
28. J. W. Moon and L. Moser. On cliques in graphs. Israel Journal of Mathematics 3: 23-28 (1965).
29. R. Niedermeier. Invitation to Fixed Parameter Algorithms. Oxford University Press, Oxford (2006).
30. R. Niedermeier and P. Rossmanith. An efficient fixed parameter algorithm for 3-Hitting Set. Journal of Discrete Algorithms 1(1): 89-102 (2003).
31. V. Raman and S. Saurabh. Parameterized algorithms for feedback set problems and their duals in tournaments. Theoretical Computer Science 351(3): 446-458 (2006).
32. V. Raman and S. Saurabh. Triangles, 4-cycles and parameterized (in-)tractability. To appear in Pro-ceedings of the 10th Scandinavian Workshop on Algorithm Theory (SWAT). Lecture Notes in Computer Science (2006).
33. V. Raman, S. Saurabh and S. Sikdar. Improved exact exponential algorithms for vertex bipartization and other problems. In Proceedings of the 9th Italian Conference on Theoretical Computer Science (ICTCS), pp. 375-389. Lecture Notes in Computer Science 3701. Springer-Verlag, Berlin (2005).
34. I. Razgon. Exact computation of maximum induced forest. To appear in Proceedings of the 10th Scan-dinavian Workshop on Algorithm Theory (SWAT). Lecture Notes in Computer Science (2006).
35. B. Randerath and I. Schiermeyer. Exact Algorithms for Minimum Dominating Set. Technical Report, zaik-469, Zentrum für Angewandte Informatik, Köln (2004).
36. B. Reed, K. Smith and A. Vetta. Finding odd cycle transversals. Operations Research Letters 32: 299-301 (2004).
37. n/4)? Technical Report 1251-01, LaBRI, Université Bordeaux I (2001).
38. M. Wahlström. Exact algorithms for finding minimum transversals in rank-3 hypergraphs. Journal of Algorithms 51(2): 107-121 (2004).
39. D. B. West. Introduction to Graph Theory, second edition. Prentice-Hall, Englewood Cliffs, NJ (2001).
40. R. Williams. A new algorithm for optimal 2-constraint satisfaction, and its implications. In Proceedings of the International Colloquium on Automata, Languages and Programming (ICALP), pp. 1227-1237. Lecture Notes in Computer Science 3142. Springer-Verlag, Berlin (2004).
41. G. Woeginger. Exact algorithms for NP-hard problems: a survey. In Combinatorial OptimizationEureka\ You shrink!, pp. 155-207. Lecture Notes in Computer Science 2570. Springer-Verlag, Berlin (2003).
42. G. Woeginger. Space and time complexity of exact algorithms: some open problems. In Proceedings of the 1st International Workshop on Exact and Parameterized Algorithms (IWPEC), pp. 281-290. Lecture Notes in Computer Science 3.162. Springer-Verlag, Berlin (2004).