The Complexity of Reasoning about Spatial Congruence

Cristani, Matteo

doi:10.1613/jair.641

Cited by 21 publications

(12 citation statements)

References 18 publications

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“…PAC tractability results can also be shown for the basic binary relations in the spatial reasoning formalism of RCC-5 [15], which is closely related to set constraints, but also for other known tractable spatial constraint satisfaction problems in qualitative spatial reasoning, e.g., in [8].…”

Section: Set Constraintsmentioning

confidence: 99%

Peek arc consistency

Bodirsky

Chen

2010

Theoretical Computer Science

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This paper studies peek arc consistency, a reasoning technique that extends the wellknown arc consistency technique for constraint satisfaction. In contrast to other more costly extensions of arc consistency that have been studied in the literature, peek arc consistency requires only linear space and quadratic time and can be parallelized in a straightforward way such that it runs in linear time with a linear number of processors. We demonstrate that for various constraint languages, peek arc consistency gives a polynomial-time decision procedure for the constraint satisfaction problem. We also present an algebraic characterization of those constraint languages that can be solved by peek arc consistency, and study the robustness of the algorithm. IntroductionBackground. A basic knowledge reasoning task that has been studied in many incarnations is to decide the satisfiability of given relationships on variables, where, for instance, variables may represent objects such as temporal events or spatial regions, and relationships may express precedence, containment, overlap, disjointness, and so forth. Instances of this reasoning task can typically be modeled using the constraint satisfaction problem (CSP), a computational problem in which the input consists of a set of constraints on variables, and the question is whether or not there is an assignment to the variables satisfying all of the constraints. While the CSP is in general NP-hard, researchers have, in numerous settings, aimed to identify restricted sets of relationships under which the CSP is polynomial-time decidable; we refer to sets of relationships as constraint languages.Arc consistency is an algorithmic technique for constraint satisfaction that has been heavily studied and for which highly efficient implementations that are linear in both time and space are known. Arc consistency provides a one-sided satisfiability check. It may detect an inconsistency, which always implies that the input instance is unsatisfiable. While the converse does not hold in general, it has been shown to hold for some particular constraint languages, that is, arc consistency provides a decision procedure for satisfiability for these languages. Examples include the language of boolean Horn clauses; various graph homomorphism problems, for example, homomorphisms to orientations of finite paths [13]; and all constraint languages where satisfiability is first-order definable [1].Curiously, arc consistency typically cannot be used as a decision procedure for infinite-domain constraint languages, by which we mean constraint languages under which variables can take on infinitely many values. In many cases, a reason for this is that arc consistency performs inference by considering unary (arity 1) projections of relations, and all such projections are already equal to the full domain of the language. As an example, consider the binary relations ≤ and = interpreted over the domain of rational numbers Q. For each of these relations, both of the two possible unary projections are equal t...

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Section: Set Constraintsmentioning

confidence: 99%

Peek arc consistency

Bodirsky

Chen

2010

Theoretical Computer Science

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“…In NLP, the focus is on how to simulate situations according to the context besides the prototypical meaning of space-related prepositions. [15][16][17] In GIS, data are selected according to the user's queries in order to show, process, and analyze spatial data. 9 In AI and robotics, spatial-relation problems are concerned mainly with recognition of a spatial situation from the view of an agent or robot in search of its goal location.…”

Section: Related Researchmentioning

confidence: 99%

Hierarchical spatial relation based on a contiguity graph

Choe

Park

Pyo

2005

Int. J. Intell. Syst.

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Autonomous agents traversing a natural space need to be knowledgeable of its space configuration. The existing space models in geographic information systems and robotics, however, deal with only the topological relations among numerous types of spatial relations. We aim to develop an enhanced space model that elaborates the spatial relations with respect to their relevant physical relations. Specifically, the spatial relations in a space configuration are further characterized with the gravitation as a potential factor to affect the space configuration. The resulting space model is capable of capturing an extended set of spatial relations over existing models such as a four-intersection model.

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“…A simple constraint language whose four primitives combine notions of congruence and mereology has been defined and investigated from a computational viewpoint [50]-the primitives are EQ, CGPP, CGPPi (congruent to a proper part, and the inverse relation), and CNO (where none of the other relations hold).…”

Section: Mereogeometrymentioning

confidence: 99%

Qualitative Spatial Representation and Reasoning

2002

Qualitative Spatial Reasoning With Topological Information

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The Complexity of Reasoning about Spatial Congruence

Cited by 21 publications

References 18 publications

Peek arc consistency

Peek arc consistency

Hierarchical spatial relation based on a contiguity graph

Qualitative Spatial Representation and Reasoning

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