Effective solution of qualitative interval constraint problems
Artificial Intelligence
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Constraint Processing
A Tableau Algorithm for Description Logics with Concrete Domains and General TBoxes
Journal of Automated Reasoning
Modelling and solving temporal reasoning as propositional satisfiability
Artificial Intelligence
Combining binary constraint networks in qualitative reasoning
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
Efficient methods for qualitative spatial reasoning
Journal of Artificial Intelligence Research
Qualitative spatial and temporal reasoning: efficient algorithms for everyone
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Predicting learnt clauses quality in modern SAT solvers
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A divide-and-conquer approach for solving interval algebra networks
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Qualitative CSP, finite CSP, and SAT: comparing methods for qualitative constraint-based reasoning
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Eligible and frozen constraints for solving temporal qualitative constraint networks
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Consistency of Qualitative Constraint Networks from Tree Decompositions
TIME '11 Proceedings of the 2011 Eighteenth International Symposium on Temporal Representation and Reasoning
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
RCC8 is polynomial on networks of bounded treewidth
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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Constraint networks in qualitative spatial and temporal reasoning (QSTR) typically feature variables defined on infinite domains. Mainstream algorithms for deciding network consistency are based on searching for network refinements whose consistency is known to be tractable, either directly or by using a SAT solver. Consequently, these algorithms treat all networks effectively as complete graphs, and are not directly amenable to complexity bounds based on network structure, such as measured by treewidth, that are well known in the finite-domain case. The present paper makes two major contributions, spanning both theory and practice. First, we identify a sufficient condition under which consistency can be decided in polynomial time for networks of bounded treewidth in QSTR, and show that this condition is satisfied by a range of calculi including the Interval Algebra, Rectangle Algebra, Block Algebra, RCC8, and RCC5. Second, we apply the techniques used in establishing these results to a SAT encoding of QSTR, and obtain a new, more compact encoding which is also guaranteed to be solvable in polynomial time for networks of bounded treewidth, and which leads to a significant advance of the state of the art in solving the hardest benchmark problems.