Reasoning about qualitative temporal information
Artificial Intelligence - Special volume on constraint-based reasoning
Consistent Queries over Cardinal Directions Across Different Levels of Detail
DEXA '00 Proceedings of the 11th International Workshop on Database and Expert Systems Applications
Constraint Processing
Similarity assessment for cardinal directions between extended spatial objects
Similarity assessment for cardinal directions between extended spatial objects
Composing cardinal direction relations
Artificial Intelligence
Cardinal directions between spatial objects: the pairwise-consistency problem
Information Sciences—Informatics and Computer Science: An International Journal
On the consistency of cardinal direction constraints
Artificial Intelligence
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
Reasoning with cardinal directions: an efficient algorithm
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Combinative reasoning with RCC5 and cardinal direction relations
KSEM'07 Proceedings of the 2nd international conference on Knowledge science, engineering and management
Cardinal direction relations in 3D space
KSEM'07 Proceedings of the 2nd international conference on Knowledge science, engineering and management
Reasoning about cardinal directions between extended objects
Artificial Intelligence
Using extended cardinal direction calculus in natural language based systems
ICAISC'10 Proceedings of the 10th international conference on Artifical intelligence and soft computing: Part II
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In this paper we study a recent formal model for qualitative spatial reasoning with cardinal direction relations. We give an O(n4) algorithm to check the consistency of a network of basic cardinal constraints with variables ranging over the set of connected regions homeomorphic to the closed unit disk (which includes a wide variety of irregular-shaped regions). To the best of our knowledge, this was an open problem. A previous algorithm for a domain that includes also disconnected regions works in O(n5), but, for the problem we consider here, such an algorithm cannot be used. Using the new algorithm we also show that the problem of deciding the consistency of a network of disjunctive cardinal constraints with variables ranging over the set of connected regions is NP-Complete. Our main contribution is based on results from the field of combinatorial geometry.