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Linear Versus Polynomial Constraint Databases

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Encyclopedia of GIS

Synonyms

Linear constraint databases; First-order logic with constraints queries

Definition

The framework of constraint databases provides a rather general model for spatial databases [14]. In the constraint model, a spatial database contains a finite number of relations, that, although conceptually viewed as possibly infinite sets of points in the real space, are represented as a finite union of systems of polynomial equations and inequalities.

More specifically, in the polynomial constraint database model, a relation is defined as a boolean combination (union, intersection, complement) of subsets of some real space ℝn (in applications, typically n = 2 or 3) that are definable by polynomial constraints of the form p(x 1, …, x n ) ≥ 0, where p is a polynomial in the real variables x 1, …, x n with integer coefficients. For example, the spatial relation consisting of the set of points in the upper half of the unit disk in ℝ2 can be represented by the formula x 2 + y 2≤ 1 ⋀y≥ 0. In...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Theoretical Computer Science Group, Hasselt University and Transnational University of Limburg, Diepenbeek, Belgium

    Bart Kuijpers

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  1. Bart Kuijpers
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Shashi Shekhar (McKnight Distinguished University Professor) (McKnight Distinguished University Professor)

  2. Management Science and Information Systems Department, Rutgers Business School Newark and New Brunswick Rutgers, the State University of New Jersey, Newark, NJ, 07102, USA

    Hui Xiong (Assistant Professor) (Assistant Professor)

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Kuijpers, B. (2008). Linear Versus Polynomial Constraint Databases. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_696

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