Towards fixed-parameter tractable algorithms for abstract argumentation

Artificial Intelligence

Volumn 186, Issue , 2012, Pages 1-37

  Dvořák, Wolfgang ^a   Pichler, Reinhard ^a   Woltran, Stefan ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Abstract argumentation; Complexity; Dynamic programming; Fixed parameter tractability; Tree width

Indexed keywords

ABSTRACT ARGUMENTATION; ARGUMENTATION FRAMEWORKS; COMPLEXITY; COMPLEXITY RESULTS; COMPUTATIONAL PROBLEM; FIXED-PARAMETER TRACTABILITY; LINEAR TIME; TRACTABLE ALGORITHMS; TREE-WIDTH;

ALGORITHMS; DYNAMIC PROGRAMMING; FORESTRY;

PROBLEM SOLVING;

ALGORITHMS; COMPUTATION; FORESTRY; PROBLEM SOLVING;

EID: 84858737488     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.artint.2012.03.005     Document Type: Article

References (43)

1. E. Amir Approximation algorithms for treewidth Algorithmica 56 4 2010 448 479
2. J. Barát Directed path-width and monotonicity in digraph searching Graphs Combin. 22 2 2006 161 172
3. P. Baroni, P.E. Dunne, and M. Giacomin On extension counting problems in argumentation frameworks P. Baroni, F. Cerutti, M. Giacomin, G.R. Simari, Proceedings of the 3rd Conference on Computational Models of Argument (COMMA 10) Frontiers in Artificial Intelligence and Applications vol. 216 2010 IOS Press 63 74
4. P. Baroni, and M. Giacomin Semantics of abstract argument systems I. Rahwan, G. Simari, Argumentation in Artificial Intelligence 2009 Springer 25 44
5. P. Baroni, M. Giacomin, and G. Guida SCC-recursiveness: A general schema for argumentation semantics Artificial Intelligence 168 1-2 2005 162 210
6. D. Berwanger, A. Dawar, P. Hunter, S. Kreutzer, DAG-width and parity games, in: Proceedings of the 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS 2006), 2006, pp. 524-536.
7. H.L. Bodlaender A linear-time algorithm for finding tree-decompositions of small treewidth SIAM J. Comput. 25 6 1996 1305 1317
8. H.L. Bodlaender, and A.M.C.A. Koster Treewidth computations. I: Upper bounds Inform. and Comput. 208 2010 259 275
9. H.L. Bodlaender, and A.M.C.A. Koster Safe separators for treewidth Discrete Math. 306 3 2006 337 350
10. M. Caminada Semi-stable semantics P.E. Dunne, T.J.M. Bench-Capon, Proceedings of the 1st Conference on Computational Models of Argument (COMMA 06) Frontiers in Artificial Intelligence and Applications vol. 144 2006 IOS Press 121 130
11. M. Caminada, and D.M. Gabbay A logical account of formal argumentation Studia Logica 93 2-3 2009 109 145
12. S. Coste-Marquis, C. Devred, and P. Marquis Symmetric argumentation frameworks L. Godo, Proceedings of the 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2005) LNCS vol. 3571 2005 Springer 317 328
13. B. Courcelle The monadic second-order logic of graphs. I. Recognizable sets of finite graphs Inform. and Comput. 85 1 1990 12 75
14. B. Courcelle, J. Engelfriet, and G. Rozenberg Handle-rewriting hypergraph grammars J. Comput. System Sci. 46 2 1993 218 270
15. B. Courcelle, J.A. Makowsky, and U. Rotics Linear time solvable optimization problems on graphs of bounded clique-width Theory Comput. Syst. 33 2 2000 125 150
16. E.D. Demaine, F.V. Fomin, M.T. Hajiaghayi, and D.M. Thilikos Subexponential parameterized algorithms on bounded-genus graphs and h-minor-free graphs J. ACM 52 6 2005 866 893
17. Y. Dimopoulos, and A. Torres Graph theoretical structures in logic programs and default theories Theoret. Comput. Sci. 170 1-2 1996 209 244
18. J. Dix, S. Parsons, H. Prakken, and G.R. Simari Research challenges for argumentation Comput. Sci. Res. Develop. 23 1 2009 27 34
19. S. Doutre, and J. Mengin Preferred extensions of argumentation frameworks: Query answering and computation R. Goré, A. Leitsch, T. Nipkow, Proceedings of the 1st International Joint Conference on Automated Reasoning (IJCAR 2001) LNCS vol. 2083 2001 Springer 272 288
20. P.M. Dung On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games Artificial Intelligence 77 2 1995 321 358
21. P.M. Dung, P. Mancarella, and F. Toni Computing ideal sceptical argumentation Artificial Intelligence 171 10-15 2007 642 674
22. P.E. Dunne Computational properties of argument systems satisfying graph-theoretic constraints Artificial Intelligence 171 10-15 2007 701 729
23. P.E. Dunne The computational complexity of ideal semantics Artificial Intelligence 173 18 2009 1559 1591
24. P.E. Dunne, and T.J.M. Bench-Capon Coherence in finite argument systems Artificial Intelligence 141 1-2 2002 187 203
25. W. Dvorák, M. Morak, C. Nopp, and S. Woltran dynPARTIX - A dynamic programming reasoner for abstract argumentation CoRR 2011 arXiv:1108.4804 [cs.AI]
26. W. Dvořák, and S. Woltran Complexity of semi-stable and stage semantics in argumentation frameworks Inform. Process. Lett. 110 11 2010 425 430
27. W. Dvořák, S. Szeider, and S. Woltran Reasoning in argumentation frameworks of bounded clique-width P. Baroni, F. Cerutti, M. Giacomin, G.R. Simari, Proceedings of the 3rd Conference on Computational Models of Argument (COMMA 10) Frontiers in Artificial Intelligence and Applications vol. 216 2010 IOS Press 219 230
28. L.C. Eggan Transition graphs and the star height of regular events Michigan Math. J. 10 1963 385 397
29. U. Egly, S.A. Gaggl, and S. Woltran Answer-set programming encodings for argumentation frameworks Argum. Comput. 1 2 2010 147 177
30. J. Flum, and M. Grohe Parameterized Complexity Theory Texts in Theoretical Computer Science 2006 Springer
31. H. Gruber, Digraph complexity measures and applications in formal language theory, in: Proceedings of the 4th Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS 2008), 2008, pp. 60-67.
32. T. Hammerl, N. Musliu, Ant colony optimization for tree decompositions, in: EvoCOP, 2010, pp. 95-106.
33. P. Hunter, and S. Kreutzer Digraph measures: Kelly decompositions, games, and orderings Theoret. Comput. Sci. 399 3 2008 206 219
34. M. Jakl, R. Pichler, S. Woltran, Answer-set programming with bounded treewidth, in: Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI 2009), 2009, pp. 816-822.
35. T. Johnson, N. Robertson, P.D. Seymour, and R. Thomas Directed tree-width J. Combin. Theory Ser. B 82 1 2001 138 154
36. K. Kask, A. Gelfand, L. Otten, R. Dechter, Pushing the power of stochastic greedy ordering schemes for inference in graphical models, in: Proceedings of the Twenty-Fifth Conference on Artificial Intelligence (AAAI-11), 2011.
37. T. Kloks Treewidth, Computations and Approximations Lecture Notes in Computer Science vol. 842 1994 Springer
38. S. Modgil, and M. Caminada Proof theories and algorithms for abstract argumentation frameworks I. Rahwan, G. Simari, Argumentation in Artificial Intelligence 2009 Springer 105 129
39. N. Musliu An iterative heuristic algorithm for tree decomposition Recent Advances in Evolutionary Computation for Combinatorial Optimization Studies in Computational Intelligence vol. 153 2008 Springer 133 150
40. N. Robertson, and P.D. Seymour Graph minors. II. Algorithmic aspects of tree-width J. Algorithms 7 3 1986 309 322
41. L.G. Valiant The complexity of enumeration and reliability problems SIAM J. Comput. 8 3 1979 410 421
42. F. van den Eijkhof, H.L. Bodlaender, and A.M.C.A. Koster Safe reduction rules for weighted treewidth Algorithmica 47 2 2007 139 158
43. B. Verheij, Two approaches to dialectical argumentation: Admissible sets and argumentation stages, in: J. Meyer, L. van der Gaag (Eds.), Proceedings of the 8th Dutch Conference on Artificial Intelligence (NAIC 96), 1996, pp. 357-368.