Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
On the relationship between circumscription and negation as failure
Artificial Intelligence
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
The complexity of logic-based abduction
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Parameterized Complexity
Generalized hypertree decompositions: np-hardness and tractable variants
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Monadic datalog over finite structures with bounded treewidth
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On computing all abductive explanations from a propositional Horn theory
Journal of the ACM (JACM)
Fast Counting with Bounded Treewidth
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
Tractable Optimization Problems through Hypergraph-Based Structural Restrictions
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Belief Revision with Bounded Treewidth
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Efficient datalog abduction through bounded treewidth
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Abduction with bounded treewidth: from theoretical tractability to practically efficient computation
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Bounded treewidth as a key to tractability of knowledge representation and reasoning
Artificial Intelligence
Answer-set programming with bounded treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Tractable database design and datalog abduction through bounded treewidth
Information Systems
Monadic datalog over finite structures of bounded treewidth
ACM Transactions on Computational Logic (TOCL)
The Complexity of Handling Minimal Solutions in Logic-Based Abduction
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
A benchmark diagnostic model generation system
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on model-based diagnostics
A dynamic-programming based ASP-solver
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
Algorithms and complexity results for persuasive argumentation
Artificial Intelligence
Parameterized complexity and fixed-parameter tractability of description logic reasoning
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Evaluating tree-decomposition based algorithms for answer set programming
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
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Several forms of reasoning in AI - like abduction, closed world reasoning, circumscription, and disjunctive logic programming - are well known to be intractable. In fact, many of the relevant problems are on the second or third level of the polynomial hierarchy. In this paper, we show how the powerful notion of treewidth can be fruitfully applied to this area. In particular, we show that all these problems become tractable (actually, even solvable in linear time), if the treewidth of the involved formulae (or of the disjunctive logic programs, resp.) is bounded by some constant. Experiments with a prototype implementation prove the feasibility of this new approach, in principle, and also give us hints for necessary improvements. In many areas of computer science, bounded treewidth has been shown to be a realistic and practically relevant restriction. We thus argue that bounded treewidth is a key factor in the development of efficient algorithms also in knowledge representation and reasoning - despite the high worst case complexity of the problems of interest.