Fixed-parameter tractability

Frontiers in Artificial Intelligence and Applications

Volumn 185, Issue 1, 2009, Pages 425-454

  Samer, Marko ^a   Szeider, Stefan ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

FORMAL LOGIC; PARALLEL PROCESSING SYSTEMS;

COMPLEXITY ANALYSIS; FINE GRAINED; FIXED-PARAMETER TRACTABILITY; INPUT SIZE; PARAMETERIZED COMPLEXITY; POLYNOMIAL-TIME; PROBLEM INSTANCES; SECONDARY MEASUREMENTS; THEORETICAL FRAMEWORK; TWO-DIMENSIONAL;

POLYNOMIAL APPROXIMATION;

EID: 72949086206     PISSN: 09226389     EISSN: 18798314     Source Type: Book Series    
DOI: 10.3233/978-1-58603-929-5-425     Document Type: Article

References (78)

1. S. Arnborg, D. G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM Journal on Algebraic and Discrete Methods, 8(2):277-284, 1987.
2. R. Aharoni and N. Linial. Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas. Journal of Combinatorial Theory, Series A, 43(2):196-204, 1986.
3. E. Amir. Efficient approximations for triangulation of minimum treewidth. In Proc. 17th Conference on Uncertainty in Artificial Intelligence (UAI'01), pages 7-15. Morgan Kaufmann, 2001.
4. F. Bacchus, S. Dalmao, and T. Pitassi. Algorithms and complexity results for #SAT and Bayesian inference. In Proc. 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03), pages 340-351. IEEE Computer Society, 2003.
5. H. L. Bodlaender, F. V. Fomin, A. M. C. A. Koster, D. Kratsch, and D. M. Thilikos. On exact algorithms for treewidth. In Proc. 14th Annual European Symposium on Algorithms (ESA'06), volume 4168 of LNCS, pages 672-683. Springer-Verlag, 2006.
6. H. L. Bodlaender, J. R. Gilbert, H. Hafsteinsson, and T. Kloks. Approximating treewidth, pathwidth, frontsize, and shortest elimination tree. Journal of Algorithms, 18(2):238-255, 1995.
7. H. L. Bodlaender and T. Kloks. Efficient and constructive algorithms for the pathwidth and treewidth of graphs. Journal of Algorithms, 21(2):358-402, 1996.
8. V. Bouchitt́e, D. Kratsch, H. Müller, and I. Todinca. On treewidth approximations. Discrete Applied Mathematics, 136(2-3):183-196, 2004.
9. H. L. Bodlaender. A tourist guide through treewidth. Acta Cybernetica, 11(1-2):1-22, 1993.
10. H. L. Bodlaender. A linear-time algorithm for finding treedecompositions of small treewidth. SIAM Journal of Computing, 25(6):1305-1317, 1996.
11. H. L. Bodlaender. Discovering treewidth. In Proc. 31st Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM' 05), volume 3381 of LNCS, pages 1-16. Springer-Verlag, 2005.
12. F. Bacchus and J. Winter. Effective preprocessing with hyperresolution and equality reduction. In Proc. 6th International Conference on Theory and Applications of Satisfiability Testing (SAT'03), Selected and Revised Papers, volume 2919 of LNCS, pages 341-355. Springer-Verlag, 2004.
13. L. Cai, J. Chen, R. G. Downey, and M. R. Fellows. Advice classes of parameterized tractability. Annals of Pure and Applied Logic, 84(1):119-138, 1997.
14. Y. Crama, O. Ekin, and P. L. Hammer. Variable and term removal from Boolean formulae. Discrete Applied Mathematics, 75(3):217-230, 1997.
15. B. Courcelle, J. Engelfriet, and G. Rozenberg. Handle-rewriting hypergraph grammars. Journal of Computer and System Sciences, 46(2):218-270, 1993.
16. M. Cesati. Compendium of parameterized problems. URL: http://bravo.ce.uniroma2.it/home/cesati/research/compendium. pdf, September 2006.
17. D. Cohen, P. Jeavons, and M. Gyssens. A unified theory of structural tractability for constraint satisfaction problems. Journal of Computer and System Sciences, 74(5):721-743, 2008.
18. J. Chen and I. A. Kanj. Improved exact algorithms for MAX-SAT. Discrete Applied Mathematics, 142(1-3):17-27, 2004.
19. J. Chen, I. A. Kanj, and W. Jia. Vertex cover: Further observations and further improvements. Journal of Algorithms, 41(2):280-301, 2001.
20. J. Chen, I. A. Kanj, and G. Xia. Improved parameterized upper bounds for vertex cover. In Proc. 31st International Symposium on Mathematical Foundations of Computer Science (MFCS'06), volume 4162 of LNCS, pages 238-249. Springer-Verlag, 2006.
21. B. Courcelle, J. A. Makowsky, and U. Rotics. On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic. Discrete Applied Mathematics, 108(1-2):23-52, 2001.
22. B. Courcelle and S. Olariu. Upper bounds to the clique-width of graphs. Discrete Applied Mathematics, 101(1-3):77-114, 2000.
23. B. Courcelle. The monadic second-order logic of graphs: Definable sets of finite graphs. In Proc. 14th International Workshop on Graph- Theoretic Concepts in Computer Science (WG'88), volume 344 of LNCS, pages 30-53. Springer-Verlag, 1988.
24. R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer-Verlag, 1999.
25. B. N. Dilkina, C. P. Gomes, and A. Sabharwal. Tradeoffs in the complexity of backdoor detection. In Proc. 13th International Conference on Principles and Practice of Constraint Programming (CP'07), volume 4741 of LNCS, pages 256-270. Springer-Verlag, 2007.
26. S. Dantchev, B. Martin, and S. Szeider. Parameterized proof complexity. In Proc. 48th Annual Symposium on Foundations of Computer Science (FOCS'07), pages 150-160. IEEE Computer Society, 2007.
27. S. Dantchev, B. Martin, and S. Szeider. Parameterized proof complexity: A complexity gap for parameterized tree-like resolution. Technical Report TR07-001, Electronic Colloquium on Computational Complexity (ECCC), January 2007.
28. J. Flum and M. Grohe. Parameterized Complexity Theory. Springer- Verlag, 2006.
29. H. Fleischner, O. Kullmann, and S. Szeider. Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference. Theoretical Computer Science, 289(1):503-516, 2002.
30. F. V. Fomin, D. Kratsch, and I. Todinca. Exact (exponential) algorithms for treewidth and minimum fill-in. In Proc. 31st International Colloquium on Automata, Languages and Programming (ICALP'04), volume 3142 of LNCS, pages 568-580. Springer-Verlag, 2004.
31. E. Fischer, J. A. Makowsky, and E. V. Ravve. Counting truth assignments of formulas of bounded tree-width or cliquewidth. Discrete Applied Mathematics, 156(4):511-529, 2008. DOI: 10.1016/j.dam.2006.06.020.
32. M. R. Fellows, S. Szeider, and G. Wrightson. On finding short resolution refutations and small unsatisfiable subsets. Theoretical Computer Science, 351(3):351-359, 2006.
33. J. Franco and A. Van Gelder. A perspective on certain polynomial time solvable classes of satisfiability. Discrete Applied Mathematics, 125(2):177-214, 2003.
34. M. R. Garey and D. R. Johnson. Computers and Intractability. W. H. Freeman and Company, 1979.
35. G. Gottlob, N. Leone, and F. Scarcello. Hypertree decompositions and tractable queries. Journal of Computer and System Sciences, 64(3):579-627, 2002.
36. M. Grohe and D. Marx. Constraint solving via fractional edge covers. In Proc. 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'06), pages 289-298. ACM Press, 2006.
37. J. Guo and R. Niedermeier. Invitation to data reduction and problem kernelization. ACM SIGACT News, 38(2):31-45, 2007.
38. G. Gottlob and S. Szeider. Fixed-parameter algorithms for artificial intelligence, constraint satisfaction, and database problems. The Computer Journal, 51(3):303-325, 2008. DOI: 10.1093/comjnl/bxm056. (Pubitemid 351649935)
39. G. Gottlob, F. Scarcello, and M. Sideri. Fixed-parameter complexity in AI and nonmonotonic reasoning. Artificial Intelligence, 138(1- 2):55-86, 2002.
40. J. E. Hopcroft and R. M. Karp. An n5/2 algorithm for maximum matchings in bipartite graphs. SIAM Journal of Computing, 2(4):225-231, 1973.
41. R. Impagliazzo, R. Paturi, and F. Zane. Which problems have strongly exponential complexity. Journal of Computer and System Sciences, 63(4):512-530, 2001.
42. K. Iwama. CNF-satisfiability test by counting and polynomial average time. SIAM Journal of Computing, 18(2):385-391, 1989.
43. D. S. Johnson. A catalog of complexity classes. In J. van Leewen, editor, Handbook of Theoretical Computer Science, volume A, chapter 2, pages 67-161. Elsevier Science Publishers, 1990.
44. H. Kleine Büning and T. Lettmann. Propositional logic: Deduction and algorithms. Cambridge University Press, 1999.
45. A. M. C. A. Koster, H. L. Bodlaender, and S. P. M. van Hoesel. Treewidth: Computational experiments. Technical Report ZIB 01-38, Konrad-Zuse-Zentrum für Informationstechnik Berlin, 2001.
46. A. M. C. A. Koster, H. L. Bodlaender, and S. P. M. van Hoesel. Treewidth: Computational experiments. Electronic Notes in Discrete Mathematics, 8:54-57, 2001.
47. H. Kleine Büning. On subclasses of minimal unsatisfiable formulas. Discrete Applied Mathematics, 107(1-3):83-98, 2000.
48. T. Kloks. Treewidth: Computations and Approximations. Springer- Verlag, 1994.
49. P. G. Kolaitis and M. Y. Vardi. Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, 61(2):302-332, 2000.
50. H. Kleine Büning and X. Zhao. Satisfiable formulas closed under replacement. Electronic Notes in Discrete Mathematics, 9:48-58, 2001.
51. H. R. Lewis. Renaming a set of clauses as a Horn set. Journal of the ACM, 25(1):134-135, 1978.
52. L. Lov́asz and M. D. Plummer. Matching Theory. Number 29 in Annals of Discrete Mathematics. North-Holland Publishing Co., Amsterdam, 1986.
53. M. Mahajan and V. Raman. Parameterizing above guaranteed values: MaxSat and MaxCut. Journal of Algorithms, 31(2):335-354, 1999.
54. M. Mahajan, V. Raman, and S. Sikdar. Parameterizing MAX SNP problems above guaranteed values. In Proc. 2nd International Workshop on Parameterized and Exact Computation (IWPEC'06), volume 4169 of LNCS, pages 38-49. Springer-Verlag, 2006.
55. R. Niedermeier. Invitation to Fixed-Parameter Algorithms. Number 31 in Oxford Lecture Series in Mathematics and Its Applications. Oxford University Press, 2006.
56. R. Niedermeier and P. Rossmanith. An efficient fixed-parameter algorithm for 3-hitting set. Journal of Discrete Algorithms, 1(1):89-102, 2003.
57. N. Nishimura, P. Ragde, and S. Szeider. Detecting backdoor sets with respect to Horn and binary clauses. In Proc. 7th International Conference on Theory and Applications of Satisfiability Testing (SAT'04), pages 96-103. Informal Proceedings, 2004.
58. N. Nishimura, P. Ragde, and S. Szeider. Solving #SAT using vertex covers. Acta Informatica, 44(7-8):509-523, 2007.
59. S.-i. Oum. Approximating rank-width and clique-width quickly. In Proc. 31st International Workshop on Graph-Theoretic Concepts in Computer Science (WG'05), volume 3787 of LNCS, pages 49-58. Springer-Verlag, 2005.
60. C. H. Papadimitriou and D.Wolfe. The complexity of facets resolved. Journal of Computer and System Sciences, 37(1):2-13, 1988.
61. B. A. Reed. Finding approximate separators and computing treewidth quickly. In Proc. 24th Annual ACM symposium on Theory of Computing (STOC'92), pages 221-228. ACM Press, 1992.
62. I. Razgon and B. O'Sullivan. Almost 2-SAT is fixed-parameter tractable. In Proc. 35th International Colloquium on Automata, Languages and Programming (ICALP'08), Track A: Algorithms, Automata, Complexity, and Games, volume 5125 of LNCS, pages 551- 562. Springer-Verlag, 2008.
63. D. Roth. On the hardness of approximate reasoning. Artificial Intelligence, 82(1-2):273-302, 1996.
64. N. Robertson and P. D. Seymour. Graph minors X. Obstructions to tree-decomposition. Journal of Combinatorial Theory, Series B, 52(2):153-190, 1991.
65. D. J. Rose, R. E. Tarjan, and G. S. Lueker. Algorithmic aspects of vertex elimination on graphs. SIAM Journal of Computing, 5(2):266-283, 1976.
66. M. Samer and S. Szeider. Constraint satisfaction with bounded treewidth revisited. Submitted for publication. Preliminary version published in Proc. 12th International Conference on Principles and Practice of Constraint Programming (CP'06), volume 4204 of LNCS, pages 499-513. Springer-Verlag, 2006.
67. M. Samer and S. Szeider. Algorithms for propositional model counting. In Proc. 14th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR'07), volume 4790 of LNCS, pages 484-498. Springer-Verlag, 2007.
68. M. Samer and S. Szeider. Backdoor sets of quantified Boolean formulas. In Proc. 10th International Conference on Theory and Applications of Satisfiability Testing (SAT'07), volume 4501 of LNCS, pages 230-243. Springer-Verlag, 2007.
69. M. Samer and S. Szeider. Backdoor trees. In Proc. 23rd AAAI Conference on Artificial Intelligence (AAAI'08), pages 363-368. AAAI Press, 2008.
70. S. Szeider. Minimal unsatisfiable formulas with bounded clausevariable difference are fixed-parameter tractable. Journal of Computer and System Sciences, 69(4):656-674, 2004.
71. S. Szeider. On fixed-parameter tractable parameterizations of SAT. In Proc. 6th International Conference on Theory and Applications of Satisfiability Testing (SAT'03), Selected and Revised Papers, volume 2919 of LNCS, pages 188-202. Springer-Verlag, 2004.
72. S. Szeider. Backdoor sets for DLL subsolvers. Journal of Automated Reasoning, 35(1-3):73-88, 2005. Reprinted as Chapter 4 of the book "SAT 2005 - Satisfiability Research in the Year 2005", edited by E. Giunchiglia and T. Walsh, Springer-Verlag, 2006.
73. S. Szeider. Matched formulas and backdoor sets. Journal on Satisfiability, Boolean Modeling and Computation, 6:1-12, 2008.
74. R. E. Tarjan and M. Yannakakis. Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs. SIAM Journal of Computing, 13(3):566-579, 1984.
75. Y. Villanger. Improved exponential-time algorithms for treewidth and minimum fill-in. In Proc. 7th Latin American Symposium on Theoretical Informatics (LATIN'06), volume 3887 of LNCS, pages 800-811. Springer-Verlag, 2006.
76. R. Williams, C. P. Gomes, and B. Selman. On the connections between backdoors, restarts, and heavy-tailedness in combinatorial search. In Proc. 6th International Conference on Theory and Applications of Satisfiability Testing (SAT'03), pages 222-230. Informal Proceedings, 2003.
77. G. J. Woeginger. Exact algorithms for NP-hard problems: A survey. In Proc. 5th International Workshop on Combinatorial Optimization (AUSSOIS'01) - "Eureka, You Shrink!", Revised Papers, volume 2570 of LNCS, pages 185-208. Springer-Verlag, 2003.
78. M. Yannakakis. Algorithms for acyclic database schemes. In Proc. 7th International Conference on Very Large Data Bases (VLDB'81), pages 81-94. IEEE Computer Society, 1981.