Characterization and recognition of partial 3-trees
SIAM Journal on Algebraic and Discrete Methods
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
The complexity of Boolean networks
The complexity of Boolean networks
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Easy problems for tree-decomposable graphs
Journal of Algorithms
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
Graph theoretical structures in logic programs and default theories
Theoretical Computer Science
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
An abstract, argumentation-theoretic approach to default reasoning
Artificial Intelligence
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Reasoning Model Based on the Production of Acceptable Arguments
Annals of Mathematics and Artificial Intelligence
On the computational complexity of assumption-based argumentation for default reasoning
Artificial Intelligence
Coherence in finite argument systems
Artificial Intelligence
Dynamic Programming on Graphs with Bounded Treewidth
ICALP '88 Proceedings of the 15th International Colloquium on Automata, Languages and Programming
Linear time algorithm for isomorphism of planar graphs (Preliminary Report)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Two party immediate response disputes: properties and efficiency
Artificial Intelligence
Graphs and Hypergraphs
SCC-recursiveness: a general schema for argumentation semantics
Artificial Intelligence
Dialectic proof procedures for assumption-based, admissible argumentation
Artificial Intelligence
Audiences in argumentation frameworks
Artificial Intelligence
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
IEEE Transactions on Computers
Complexity Properties of Restricted Abstract Argument Systems
Proceedings of the 2006 conference on Computational Models of Argument: Proceedings of COMMA 2006
Symmetric argumentation frameworks
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Argumentation in artificial intelligence
Artificial Intelligence
Abstract Argumentation Scheme Frameworks
AIMSA '08 Proceedings of the 13th international conference on Artificial Intelligence: Methodology, Systems, and Applications
Computational Complexity of Semi-stable Semantics in Abstract Argumentation Frameworks
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Inconsistency tolerance in weighted argument systems
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
The Computational Complexity of Ideal Semantics I: Abstract Argumentation Frameworks
Proceedings of the 2008 conference on Computational Models of Argument: Proceedings of COMMA 2008
Theoretical and Computational Properties of Preference-based Argumentation
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Manifold Answer-Set Programs for Meta-reasoning
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
A computational analysis of the tournament equilibrium set
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
The computational complexity of ideal semantics
Artificial Intelligence
Nonmanipulable selections from a tournament
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Complexity of semi-stable and stage semantics in argumentation frameworks
Information Processing Letters
Minimal retentive sets in tournaments
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
Tractability in Value-based Argumentation
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
Computation with varied-strength attacks in abstract argumentation frameworks
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
Reasoning in Argumentation Frameworks of Bounded Clique-Width
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
Algorithms and Complexity Results for Persuasive Argumentation
Proceedings of the 2010 conference on Computational Models of Argument: Proceedings of COMMA 2010
WizArg: Visual Argumentation Framework Solving Wizard
Proceedings of the 2010 conference on Artificial Intelligence Research and Development: Proceedings of the 13th International Conference of the Catalan Association for Artificial Intelligence
Weighted argument systems: Basic definitions, algorithms, and complexity results
Artificial Intelligence
On the resolution-based family of abstract argumentation semantics and its grounded instance
Artificial Intelligence
Algorithms and complexity results for persuasive argumentation
Artificial Intelligence
Dynamics of argumentation systems: A division-based method
Artificial Intelligence
Manifold answer-set programs and their applications
Logic programming, knowledge representation, and nonmonotonic reasoning
A new approach for preference-based argumentation frameworks
Annals of Mathematics and Artificial Intelligence
Augmenting tractable fragments of abstract argumentation
Artificial Intelligence
Towards fixed-parameter tractable algorithms for abstract argumentation
Artificial Intelligence
On the complexity of computing the justification status of an argument
TAFA'11 Proceedings of the First international conference on Theory and Applications of Formal Argumentation
On the fixed-parameter tractability of composition-consistent tournament solutions
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Parametric properties of ideal semantics
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Augmenting tractable fragments of abstract argumentation
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
The Multivariate Algorithmic Revolution and Beyond
Abstract argumentation via monadic second order logic
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Toward incremental computation of argumentation semantics: A decomposition-based approach
Annals of Mathematics and Artificial Intelligence
Structural properties for deductive argument systems
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Complexity-sensitive decision procedures for abstract argumentation
Artificial Intelligence
Algorithms for decision problems in argument systems under preferred semantics
Artificial Intelligence
Argumentation frameworks as constraint satisfaction problems
Annals of Mathematics and Artificial Intelligence
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One difficulty that arises in abstract argument systems is that many natural questions regarding argument acceptability are, in general, computationally intractable having been classified as complete for classes such as np, co-np, and . In consequence, a number of researchers have considered methods for specialising the structure of such systems so as to identify classes for which efficient decision processes exist. In this paper the effect of a number of graph-theoretic restrictions is considered: k-partite systems (k≥2) in which the set of arguments may be partitioned into k sets each of which is conflict-free; systems in which the numbers of attacks originating from and made upon any argument are bounded; planar systems; and, finally, those of k-bounded treewidth. For the class of bipartite graphs, it is shown that determining the acceptability status of a specific argument can be accomplished in polynomial-time under both credulous and sceptical semantics. In addition we establish the existence of polynomial time methods for systems having bounded treewidth when deciding the following: whether a given (set of) arguments is credulously accepted; if the system has a non-empty preferred extension; has a stable extension; is coherent; has at least one sceptically accepted argument. In contrast to these positive results, however, deciding whether an arbitrary set of arguments is "collectively acceptable" remains NP-complete in bipartite systems. Furthermore for both planar and bounded degree systems the principal decision problems are as hard as the unrestricted cases. In deriving these latter results we introduce various concepts of "simulating" a general argument system by a restricted class so allowing any argument system to be translated to one which has both bounded degree and is planar. Finally, for the development of basic argument systems to so-called "value-based frameworks", we present results indicating that decision problems known to be intractable in their most general form remain so even under quite severe graph-theoretic restrictions. In particular the problem of deciding "subjective acceptability" continues to be NP-complete even when the underlying graph is a binary tree.