On the desirability and limitations of linear spatial database models

Vandeurzen, Luc; Gyssens, Marc; Gucht, Dirk Van

doi:10.1007/3-540-60159-7_2

Cited by 24 publications

(14 citation statements)

References 21 publications

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“…A simple query \return the convex hull of all the vertices x with k x k< 1" does always return a convex polytope. This query must be written in a rather expressive language: it can be expressed in FO + Poly but not FO + Lin 43]. Now, our question is: can we ensure in some way that a class of FO + Poly programs preserves a given property, like being a convex polytope?…”

Section: Preserving Geometric Properties Of Constraint Databasesmentioning

confidence: 99%

“…At the same time, the extension of relational calculus with linear constraints has severely limited power as a query language, see 2,29]. Thus, it appears to be natural to use a more powerful language, such as relational calculus with polynomial constraints, to query databases represented by linear constraints 43]. As soon as the class of constraints used in queries is more general than the class used to de ne databases, we encounter the safety/closure property again: the output of a query using polynomial constraints may fail to be de nable with linear constraints alone!…”

Section: Introductionmentioning

confidence: 99%

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Safe constraint queries

Benedikt¹,

Libkin²

1998

Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

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We extend some of the classical characterization theorems of relational database theory | particularly those related to query safety | to the context where database elements come with xed interpreted structure, and where formulae over elements of that structure can be used in queries. We show that the addition of common interpreted functions such as real addition and multiplication to the relational calculus preserves important characterization theorems of the relational calculus, and also preserves certain combinatorial properties of queries. Our main result of the rst kind is that there is a syntactic characterization of the collection of safe queries over the relational calculus supplemented by a wide class of interpreted functions | a class that includes addition, multiplication, and exponentiation | and that this characterization gives us an interpreted analog of the concept of range-restricted query from the uninterpreted setting. Furthermore, our range-restricted queries are particularly intuitive for the relational calculus with real arithmetic, and give a natural syntax for safe queries in the presence of polynomial functions. We use these characterizations to show that safety is decidable for Boolean combinations of conjunctive queries for a large class of interpreted structures. We show a dichotomy theorem that sets a polynomial bound on the growth of the output of a query that might refer to addition, multiplication and exponentiation.We apply the above results for nite databases to get results on constraint databases, representing potentially in nite objects. We start by getting syntactic characterizations of the queries on constraint databases that preserve geometric conditions in the constraint data model. We consider classes of convex polytopes, polyhedra, and compact semi-linear sets, the latter corresponding to many spatial applications. We show how to give an e ective syntax to safe queries, and prove that for conjunctive queries the preservation properties are decidable.

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Section: Preserving Geometric Properties Of Constraint Databasesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Safe constraint queries

Benedikt¹,

Libkin²

1998

Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems

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“…In existing implementations of the constraint model, such as the DEDALE system [15,16,17], the constraints are restricted to linear polynomial constraints, and the sets definable in this restricted model are called semi-linear. It is argued that linear polynomial constraints provide a sufficiently general framework for spatial database applications [17,40]. Indeed, in one of the main application domains, geographical information systems, linear approximations are used to model geometrical objects (for an overview of this field since the early '90s, see [1,7,10,21,22,37]).…”

Section: Introductionmentioning

confidence: 99%

First‐Order Languages Expressing Constructible Spatial Database Queries

et al. 2007

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Abstract. The research presented in this paper is situated in the framework of constraint databases introduced by Kanellakis, Kuper, and Revesz in their seminal paper of 1990, specifically, the language with real polynomial constraints (FO + poly). For reasons of efficiency, this model is implemented with only linear polynomial constraints, but this limitation to linear polynomial constraints has severe implications on the expressive power of the query language. In particular, when used for modeling spatial data, important queries that involve Euclidean distance are not expressible. The aim of this paper is to identify a class of two-dimensional constraint databases and a query language within the constraint model that go beyond the linear model and allow the expression of queries concerning distance. We seek inspiration in the Euclidean constructions, i.e., constructions by ruler and compass. We first present a programming language that captures exactly the first-order ruler-and-compass constructions that are expressible in a first-order language with real polynomial constraints. If this language is extended with a while operator, we obtain a language that is complete for all ruler-and-compass constructions in the plane. We then transform this language in a natural way into a query language on finite point databases, but this language turns out to have the same expressive power as FO + poly and is therefore too powerful for our purposes. We then consider a safe fragment of this language and use this to construct a query language that allows the expression of Euclidean distance without having the full power of FO + poly.

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“…Several authors have argued that the restriction to linear polynomial constraints provides a sufficiently general framework for spatial database applications [15,29,30]. Indeed, in geographic information systems (GIS), which is one of the main application areas for spatial databases, linear approximations are used to model spatial objects (for an overview of this field since the early 90's we refer to [1,6,9,17,18,27]).…”

Section: Introductionmentioning

confidence: 99%

Linear approximation of planar spatial databases using transitive-closure logic

Geerts

Kuijpers

2000

Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems - PODS '00

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We consider spatial databases in the plane that can be defined by polynomial constraint formulas. Motivated by applications in geographic information systems, we investigate linear approximations of spatial databases and study in which language they can be expressed effectively. Specifically, we show that they cannot be expressed in the standard first-order query language for polynomial constraint databases but that an extension of this first-order language with transitive closure suffices to express the approximation query in an effective manner. Furthermore, we introduce an extension of transitive-closure logic and show that this logic is complete for the computable queries on linear spatial databases. This result together with our first result implies that this extension of transitive-closure logic can express all computable topological queries on arbitrary spatial databases in the plane.

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On the desirability and limitations of linear spatial database models

Cited by 24 publications

References 21 publications

Safe constraint queries

Safe constraint queries

First‐Order Languages Expressing Constructible Spatial Database Queries

Linear approximation of planar spatial databases using transitive-closure logic

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