Exact and approximate reasoning about temporal relations
Computational Intelligence
Artificial Intelligence - Special issue on knowledge representation
Effective solution of qualitative interval constraint problems
Artificial Intelligence
Reasoning about qualitative temporal information
Artificial Intelligence - Special volume on constraint-based reasoning
Complexity and algorithms for reasoning about time: a graph-theoretic approach
Journal of the ACM (JACM)
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Synthesizing constraint expressions
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Fast algebraic methods for interval constraint problems
Annals of Mathematics and Artificial Intelligence
SAT-Encodings, Search Space Structure, and Local Search Performance
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Solving the Round Robin Problem Using Propositional Logic
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
SAT-Based Procedures for Temporal Reasoning
ECP '99 Proceedings of the 5th European Conference on Planning: Recent Advances in AI Planning
A Symbolic Approach to Interval Constraint Problems
AISMC-1 Proceedings of the International Conference on Artificial Intelligence and Symbolic Mathematical Computation
Constraint Processing
Efficient solution techniques for disjunctive temporal reasoning problems
Artificial Intelligence
A Local Search Approach to Modelling and Solving Interval Algebra Problems
Journal of Logic and Computation
Additive versus multiplicative clause weighting for SAT
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Old resolution meets modern SLS
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
SAT-based versus CSP-based constraint weighting for satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
The design and experimental analysis of algorithms for temporal reasoning
Journal of Artificial Intelligence Research
Efficient methods for qualitative spatial reasoning
Journal of Artificial Intelligence Research
Ten challenges in propositional reasoning and search
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Solving non-Boolean satisfiability problems with stochastic local search
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Pushing the envelope: planning, propositional logic, and stochastic search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Towards an efficient SAT encoding for temporal reasoning
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
A SAT-based decision procedure for the boolean combination of difference constraints
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Finite Satisfiability in Infinite-Valued Łukasiewicz Logic
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
A divide-and-conquer approach for solving interval algebra networks
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
AI'10 Proceedings of the 23rd Canadian conference on Advances in Artificial Intelligence
Decomposition and tractability in qualitative spatial and temporal reasoning
Artificial Intelligence
Spatial reasoning with rectangular cardinal relations
Annals of Mathematics and Artificial Intelligence
Qualitative constraint satisfaction problems: An extended framework with landmarks
Artificial Intelligence
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Representing and reasoning about time dependent information is a key research issue in many areas of computer science and artificial intelligence. One of the best known and widely used formalisms for representing interval-based qualitative temporal information is Allen's interval algebra (IA). The fundamental reasoning task in IA is to find a scenario that is consistent with the given information. This problem is in general NP-complete. In this paper, we investigate how an interval-based representation, or IA network, can be encoded into a propositional formula of Boolean variables and/or predicates in decidable theories. Our task is to discover whether satisfying such a formula can be more efficient than finding a consistent scenario for the original problem. There are two basic approaches to modelling an IA network: one represents the relations between intervals as variables and the other represents the end-points of each interval as variables. By combining these two approaches with three different Boolean satisfiability (SAT) encoding schemes, we produced six encoding schemes for converting IA to SAT. In addition, we also showed how IA networks can be formulated into satisfiability modulo theories (SMT) formulae based on the quantifier-free integer difference logic (QF-IDL). These encodings were empirically studied using randomly generated IA problems of sizes ranging from 20 to 100 nodes. A general conclusion we draw from these experimental results is that encoding IA into SAT produces better results than existing approaches. More specifically, we show that the new point-based 1-D support SAT encoding of IA produces consistently better results than the other alternatives considered. In comparison with the six different SAT encodings, the SMT encoding came fourth after the point-based and interval-based 1-D support schemes and the point-based direct scheme. Further, we observe that the phase transition region maps directly from the IA encoding to each SAT or SMT encoding, but, surprisingly, the location of the hard region varies according to the encoding scheme. Our results also show a fixed performance ranking order over the various encoding schemes.