The complexity of recognizing polyhedral scenes
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
String graphs. II.: Recognizing string graphs is NP-hard
Journal of Combinatorial Theory Series B
String graphs requiring exponential representations
Journal of Combinatorial Theory Series B
Topological relations in the world of minimum bounding rectangles: a study with R-trees
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Maintaining knowledge about temporal intervals
Communications of the ACM
Qualitative representation of spatial knowledge in two-dimensional space
The VLDB Journal — The International Journal on Very Large Data Bases - Spatial Database Systems
Reasoning about Binary Topological Relations
SSD '91 Proceedings of the Second International Symposium on Advances in Spatial Databases
Topological queries in spatial databases
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Hierarchical reasoning about direction relations
GIS '96 Proceedings of the 4th ACM international workshop on Advances in geographic information systems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Image similarity retrieval by spatial constraints
Proceedings of the seventh international conference on Information and knowledge management
Nonplanar topological inference and political-map graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Aligning Logical and Psychological Perspectives on Diagrammatic Reasoning
Artificial Intelligence Review
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Recognizing string graphs in NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Combining topological and size information for spatial reasoning
Artificial Intelligence
Determining Consistency of Topological Relations
Constraints
Algorithms for Hierarchical Spatial Reasoning
Geoinformatica
Editorial: Efficacy of Diagrammatic Reasoning
Journal of Logic, Language and Information
Spatial Cognition and Computation
Spatial Reasoning with Topological Information
Spatial Cognition, An Interdisciplinary Approach to Representing and Processing Spatial Knowledge
Towards Cognitive Adequacy of Topological Spatial Relations
Spatial Cognition II, Integrating Abstract Theories, Empirical Studies, Formal Methods, and Practical Applications
Double-Crossing: Decidability and Computational Complexity of a Qualitative Calculus for Navigation
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
Hierarchical Topological Inference on Planar Disc Maps
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
On the Translation of Qualitative Spatial Reasoning Problems into Modal Logics
KI '99 Proceedings of the 23rd Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Qualitative spatiotemporal representation and reasoning: a computational perspective
Exploring artificial intelligence in the new millennium
Mental representation and processing of geographic knowledge
A reference framework for integrating multiple representations of geographical maps
GIS '03 Proceedings of the 11th ACM international symposium on Advances in geographic information systems
Extensionality of the RCC8 composition table
Fundamenta Informaticae
Recognizing string graphs in NP
Journal of Computer and System Sciences - STOC 2002
Composing cardinal direction relations
Artificial Intelligence
Journal of Computer and System Sciences - STOC 2001
On the consistency of cardinal direction constraints
Artificial Intelligence
Towards a practical argumentative reasoning with qualitative spatial databases
IEA/AIE'2003 Proceedings of the 16th international conference on Developments in applied artificial intelligence
On Topological Consistency and Realization
Constraints
Summarizing level-two topological relations in large spatial datasets
ACM Transactions on Database Systems (TODS)
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
A Family of Directional Relation Models for Extended Objects
IEEE Transactions on Knowledge and Data Engineering
Multiscale histograms: summarizing topological relations in large spatial datasets
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Reasoning about vague topological information
Proceedings of the sixteenth ACM conference on Conference on information and knowledge management
Reasoning on Spatial Relations between Entity Classes
GIScience '08 Proceedings of the 5th international conference on Geographic Information Science
Spatial reasoning in a fuzzy region connection calculus
Artificial Intelligence
Moving objects spatiotemporal reasoning model for battlefield analysis
ICS'08 Proceedings of the 12th WSEAS international conference on Systems
Vivid: A framework for heterogeneous problem solving
Artificial Intelligence
A complete classification of tractability in RCC-5
Journal of Artificial Intelligence Research
Efficient methods for qualitative spatial reasoning
Journal of Artificial Intelligence Research
On the consistency of cardinal direction constraints
Artificial Intelligence
Reasoning on spatial semantic integrity constraints
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
Drawing a figure in a two-dimensional plane for a qualitative representation
COSIT'07 Proceedings of the 8th international conference on Spatial information theory
Continuous constraint query evaluation for spatiotemporal streams
SSTD'07 Proceedings of the 10th international conference on Advances in spatial and temporal databases
Qualitative spatial reasoning with topological information
Qualitative spatial reasoning with topological information
Establishing similarity across multi-granular topological-relation ontologies
QuaCon'09 Proceedings of the 1st international conference on Quality of context
Topological reasoning between complex regions in databases with frequent updates
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Information Sciences: an International Journal
Reasoning about cardinal directions between extended objects: The NP-hardness result
Artificial Intelligence
Summarizing spatial relations – a hybrid histogram
APWeb'05 Proceedings of the 7th Asia-Pacific web conference on Web Technologies Research and Development
Formalization and reasoning about spatial semantic integrity constraints
Data & Knowledge Engineering
Heterogeneous spatial reasoning
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Extensionality of the RCC8 Composition Table
Fundamenta Informaticae
Qualitative Spatial Representation and Reasoning: An Overview
Fundamenta Informaticae - Qualitative Spatial Reasoning
Scalable geo-thematic query answering
ISWC'12 Proceedings of the 11th international conference on The Semantic Web - Volume Part I
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Geographical database systems deal with certain basic topological relations such as "A overlaps B" and "B contains C" between simply connected regions in the plane. It is of great interest to make sound inferences from elementary statements of this form. This problem has been identified extensively in the recent literature, but very limited progress has been made towards addressing the considerable technical difficulties involved. In this paper we study the computational problems involved in developing such an inference system. We point out that the problem has two distinct components that interact in rather complex ways: relational consistency, and planarity. We develop polynomial-time algorithms for several important special cases, and prove almost all the others to be NP-hard.