Reconstruction graphs and testing their properties in a relational spatial database

Novák, Attila; Tuza, Zs.

doi:10.1016/s0898-1221(02)00107-4

Cited by 5 publications

(14 citation statements)

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“…A more detailed explanation and also other spatial models can be found in [2]. Here we recall some parts of a review of the PLA-Model in [3]. For more detailed discussions on PLA, see (1)(2)(3).…”

Section: A the Plat-modelmentioning

confidence: 99%

“…The PLA database consists of four relations, but, as proved in [3], three of them can be reconstructed from the one denoted R3. This is the reason why the temporal extension is based on this relation, whose content is described by the following schema: R3(AREA, POINT, LINE, LABEL).…”

Section: A the Plat-modelmentioning

confidence: 99%

“…The labels are consistent with the orientation, that is, the enumeration of points and lines in the cycle corresponds to the clockwise orientation, except for the infmite area, for which the orientation is counterclockwise. (The latter distinction is made for technical reasons explained in [3].) In each row of the relation, the point and the line are incident and the line is the successor of the point in the corresponding orientation.…”

Section: A the Plat-modelmentioning

confidence: 99%

“…So, if the starting database is the PLAT-Model, then data expressiveness must be improved by attaching some data; this will be described in In [3] one can fmd an algorithm both for triangulation and drawing the graph in the plane. We extend this algorithm by giving a way of calculation for the real physical coordinates for each point during the reconstruction.…”

Section: Interoperabilitymentioning

confidence: 99%

See 3 more Smart Citations

On the interoperability problems of the spatiotemporal relational model, PLAT

Novák¹,

Ludányi

Berces

et al. 2004

Second IEEE International Conference on Computational Cybernetics, 2004. ICCC 2004.

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Since there are already tools for implementing and managing spatiotemporal data, it is worth elaborating methods for solving inter operability problems. In this paper a spatiotemporal model, PLAT is investigated from this point of view. We describe algoritbms for translating PLAT into other spatiotemporal models. It is also shown that the necessary topological information for building the PLA-or PLAT-Model can be extracted from other constraint and spatiotemporal models. These methods are useful in cases where topological properties have to be discovered, since very fast algorithms are developed in the PLA-ModeI.

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Section: A the Plat-modelmentioning

confidence: 99%

Section: A the Plat-modelmentioning

confidence: 99%

Section: A the Plat-modelmentioning

confidence: 99%

Section: Interoperabilitymentioning

confidence: 99%

See 2 more Smart Citations

On the interoperability problems of the spatiotemporal relational model, PLAT

Novák¹,

Ludányi

Berces

et al. 2004

Second IEEE International Conference on Computational Cybernetics, 2004. ICCC 2004.

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show abstract

“…A more detailed explanation and also other spatial models can be found in [6]. DetaiIed discussions of the PLA model can be found in 141, [5], [7].The PLA database consists of four relations, but three of them can be reconsbucted kom only R3 [7]. That is why the extension is based on this relation, whose content is described by the following schema:…”

mentioning

confidence: 99%

Reconstruction of planar graphs from their centered triangulations in some spatio-relational models

Novák

Tuza

IEEE 3rd International Conference on Computational Cybernetics, 2005. ICCC 2005.

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In this paper we continue the investigation of an interoperability problem and its complexity in connection with spatio-relational database models. The result, however, is also interesting from the point of view of graph theory, since the main result is that there is a liaear-time algorithm for deciding wether a given triangulation can be seen as a centered triangulation of a certain planar graph. r INTRODUCTIONIn this paper our primer goal is to complete the solution of one of the interoperability problems investigated in [ I ] . This is, how we can translate the PLA spatio-relational model into a constraint spatial model and into the Worboys' model and vice versa. The first part of this task is completely solved in [ 11, where we gave an algorithm to translate the PLA model into a constraint model and Worboys' model. Here we deal with the reverse direction: from a given Worboys' database how can one reconstruct the PLA database.In the next section we review the necessary background with the models' description. The problem is specified in Section 111. To be more precise, an abstraction is given.Due to space restrictions it is not possible to publish the practical algorithms, rather we restrict ourselves to theoretical algorithms, that have to be refined with appropriate data structure. The new results are contained in Section IV, and finally in the last section we close with some concluding remarks and future research directions. I1 BACKGROUND AND MOTIVATIONIn this section first we introduce the spatio-relational models, followed by two types of them, the PLA model and a restricted version of Worboys' and a constraint model. Then we formalize the interoperability problem. A Spatio-Relutiona~ Data ModelsIn spatio-relational databases the underlying data model is the relationat one. The content of a relation is a subset of the Cartesian product of some possible domain sets, that is, Rc DlxDlx ... xD,. One element of a relation i s called a tuple (or ntuple, in case we want to emphasize the number of domain sets). In the original relational model these domains can be just simple, not structured data. The model itself consists of the name of the relation, and the list of so-called attributes, that are the descriptive properties of an objecttwa@ztaki. hu 2 Hungary each atribute can have its data only from the corresponding domain set: Relation-name(Attribute-1 ,Attribute-2, Attribute-n) Additionally, the a-priori fixed constraints, like idetitifiers have to be represented in the relational model. If this relational model is adequate to represent physical objects, then usually it contains geometrical extent. In this case we name it as a spatial model. It also may contain time extension, then it is a temporal model. The . combination of these two is the spatiotemporal relational model. Depending on the technique of the geometricdtime extent representation, it may be an extended model, like the constraint model. This one may contain mathematical inequalities, and by the help of these, an infinite number of tuples can b...

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Extending the Spatial Relational Model PLA to Represent Trees

Novák

Tuza

Intelligent Engineering Systems and Computational Cybernetics

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Reconstruction graphs and testing their properties in a relational spatial database

Cited by 5 publications

References 5 publications

On the interoperability problems of the spatiotemporal relational model, PLAT

On the interoperability problems of the spatiotemporal relational model, PLAT

Reconstruction of planar graphs from their centered triangulations in some spatio-relational models

Extending the Spatial Relational Model PLA to Represent Trees

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