Qualitative navigation for mobile robots
Artificial Intelligence
From local to global consistency
Artificial Intelligence
Effective solution of qualitative interval constraint problems
Artificial Intelligence
A theory for qualitative spatial reasoning based on order relations
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Qualitative Spatial Representation and Reasoning Techniques
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Representation and Processing of Qualitative Orientation Knowledge
KI '97 Proceedings of the 21st Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
ER '99 Proceedings of the Workshops on Evolution and Change in Data Management, Reverse Engineering in Information Systems, and the World Wide Web and Conceptual Modeling
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
On Random Ordering Constraints
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
On random betweenness constraints
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
On random betweenness constraints
Combinatorics, Probability and Computing
Exploiting qualitative spatial neighborhoods in the situation calculus
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
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We define an algebra of ternary relations for cyclic ordering of 2D orientations. The algebra (1) is a refinement of the CYCORD theory; (2) contains 24 atomic relations, hence 224 general relations, of which the usual CYCORD relation is a particular relation; and (3) is NP-complete, which is not surprising since the CYCORD theory is. We then provide: (1) a constraint propagation algorithm for the algebra, which we show is polynomial, and complete for a subclass including all atomic relations; (2) a proof that another subclass, expressing only information on parallel orientations, is NP-complete; and (3) a solution search algorithm for a general problem expressed in the algebra.