Kuijpers, Bart, Paradaens, Jan, and van den Bussche, Jan (1995). Lossless representation of topological spatial data. In Egenhofer, M.J. and Herring, J.R., editors, Proceedings, 4th International Symposium on Large Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 1-13, Berlin. Springer.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....which, pushed by real problems, started extending traditional database management systems with at hoc features suitable to solve the problem at hand. Only recently it has been started a systematic research activity of theoretical nature focused, mainly, on problems concerning data models (e.g. [5, 13, 16, 25]) and query languages (e.g. 10, 11, 19, 21, 23] Spatial data mix two components: one concerns the description of the underlying physical entity (sometimes referred to as the thematic component) while the other concerns the geometry of the entity itself (usually referred to as the geometric ....

....Paredaens in [20] In detail, given two semi algebraic sets D 1 and D 2 , we provide a polynomial time algorithm that returns all possible isotopies i 2 I such that i(D 1 ) D 2 . Three main ingredients have been used: i) the topological invariant of a semi algebraic set D up to isotopies used in [15, 16], that is denoted as PLA(D) ii) the result that two semi algebraic sets are topologically equivalent with respect to isotopies if and only if the corresponding topological invariants are isomorphic [15] iii) the notion of boundary decomposition of the topological invariant. The first two ....

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B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In Advances in Spatial Databases (SSD'95), volume 951 of Lecture Notes in Computer Science, pages 1--13. Springer-Verlag, 1995.

....question: This work was partly performed while the first author was visiting U.C. San Diego and partly while the second author was visiting I.N.R.I.A. V.Vianu was supported in part by the NSF under grant number IRI 9221268. 1 A similar invariant for isotopy invariant properties is presented in [KPV95], see related work. 1 ffl What language L inv on topological invariants is needed in order to answer the topological queries formulated in a given query language L spatial on spatial databases ffl Is there an effective, uniform translation of topological queries in L spatial into queries in L ....

.... geometry [BKR86, KY85] While a flaw has been discovered in the complexity analysis of [BKR86] later modifications recovered, and even improved upon their upper bounds, see Renegar [Ren92] The topological invariant we use is essentially the one introduced in [PSV99] The invariants proposed in [KPV95] are also close to the topological invariants we consider, but capture isotopy generic information. Various notions of G invariance (or G genericity) for different groups G of permutations are discussed in [Par 94] They propose a spatial database model that includes spatial and thematic ....

B. Kuijpers, J. Paredaens and J. Van den Bussche. Lossless Representation of Topological Spatial Data. In Proc. Fourth Int'l. Symp. on Large Spatial Databases, 1--13, 1995.

....of spatial data. It allows to represent infinite relations by quantifier free formulae over some arithmetical domain, and to manipulate these relations in a symbolic way. An important feature of constraint databases is their ability to handle in a uniform way pointsets in arbitrary dimension [PVV94, GST94, GK96, KPV95, GK97]. Constraint databases can then be queried by standard means such as first order queries. Although this model meets our requirement of an abstract representation level, it does not solve the complexity issue. Indeed, although the data complexity has been shown to be tractable for reasonable ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M. J. Egenhofer and J. R. Herring, editors, Advances in Spatial Databases, 4th Int. Symp., SSD'95, pages 1--13. Springer, 1995.

....of data. The constraint data model, first introduced by Kanellakis, Kuper and Revesz [KKR90] offered a promising paradigm for the representation of all sorts of data in a unified framework. Linear constraints over rational numbers have been shown to fit the need of spatial data in the vector mode [KPV95, GK97]. Spatial objects, seen as infinite sets of points, could be dealt with as first class citizens with an explicit representation. This contrasts with the representation of spatial objects by their boundary in vector mode for instance, which lead to cumbersome data models with ad hoc operations, and ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M. J. Egenhofer and J. R. Herring, editors, Advances in Spatial Databases, 4th Int. Symp., SSD'95, pages 1--13. Springer, 1995.

....topological information similar to the PLA model and to our invariants has been studied in computational geometry [BKR84, KY85] Our complexity results make extensive use of these results. Closest to our topological invariants is a representation of topological information recently proposed in [KPV95], which is lossless with respect to isotopy generic 1 information and applies to a spatial model different from ours. Query languages are not considered in [KPV95] Various notions of G genericity for different groups G of permutations are discussed in [Par 94] They propose a spatial database ....

....use of these results. Closest to our topological invariants is a representation of topological information recently proposed in [KPV95] which is lossless with respect to isotopy generic 1 information and applies to a spatial model different from ours. Query languages are not considered in [KPV95]. Various notions of G genericity for different groups G of permutations are discussed in [Par 94] They propose a spatial database model that includes spatial and classical database information, and propose a calculus and an equivalent algebra. Much of the formal work related to spatial databases ....

[Article contains additional citation context not shown here]

B. Kuijpers, J. Paredaens and J. Van den Bussche. Lossless Representation of Topological Spatial Data. In Proc. Fourth Int'l. Symp. on Large Spatial Databases, 1995.

....of the theory of query languages, the result is significant because it identifies topological invariants as a class of finite structures of practical interest which is very well behaved with respect to descriptive complexity. 1 A similar invariant for isotopy invariant properties is presented in [KPV95], see related work. With respect to the second question, we focus on the translation problem for first order queries. A common language for constraint spatial databases is FO(R; We consider primarily this language on the spatial database side. On the topological invariant side, fixpoint is a ....

....invariants contain information similar to the PLA model proposed by the U.S. Census Bureau, which contains topological properties on points, lines, and areas [Cor79, Par95] The invariants can be viewed as an augmentation of the PLA model. As mentioned earlier, the invariants proposed in [KPV95] come closest to the topological invariants we consider, but capture isotopy generic information. Query languages are not considered in [KPV95] Note that partial topological annotations have been used for some time in the GIS community to speed up query evaluation (e.g. in the ARC INFO system ....

[Article contains additional citation context not shown here]

B. Kuijpers, J. Paredaens and J. Van den Bussche. Lossless Representation of Topological Spatial Data. In Proc. Fourth Int'l. Symp. on Large Spatial Databases, 1995.

....of this flavor have been considered before, this is the first time, to our knowledge, that such an invariant is shown to completely characterize inputs up to homeomorphism in the setting we consider. Closest to our invariants is a representation of topological information recently proposed in [KPV95], which is lossless with respect to isotopy generic 1 information and applies to a spatial model different from ours. We show that for inputs which are semi algebraic regions, the invariant can be computed in polynomial time (and NC ) Moreover, once this structure is computed, topological ....

....has not been formally studied. The complexity of computing topological information similar to the PLA model and to our invariants has been studied in computational geometry [BKR84, KY85] Our complexity results make extensive use of these results. As discussed earlier, the invariants proposed in [KPV95] come closest to the topological invariants we consider, but use a different spatial model and capture isotopy generic information. Query languages are not considered in [KPV95] Various notions of G genericity for different groups G of permutations are discussed in [Par 94] They propose a ....

[Article contains additional citation context not shown here]

B. Kuijpers, J. Paredaens and J. Van den Bussche. Lossless Representation of Topological Spatial Data. In Proc. Fourth Int'l. Symp. on Large Spatial Databases, 1995.

....defined as the length of its finite representation. Low upper bounds of the data complexity for both the relational calculus and inflationary Datalog with negation over constraint databases have been obtained in [KKR95] This shows the feasibility of this approach, which has been pursued in [Rev90, Kup93a, KG94, PVV94, KPV95, VGV95, CGK96, GS96b]. The goal of this paper is to investigate the expressive power of query languages over finitely representable databases. For that purpose, we study the underlying logic of constraint query languages and the corresponding model theory. Specifically, we study first order logic when the semantics is ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M. J. Egenhofer and J. R. Herring, editors, Advances in Spatial Databases, 4th Int. Symp., SSD'95, pages 1--13. Springer, 1995.

....in the complexity analysis of [BKR84] later modifications recovered, and even improved upon their upper bounds, see Renegar [Ren92] Our complexity results make extensive use of these results. Closest to our topological invariants is a representation of topological information proposed in [KPV95], which is lossless with respect to isotopy generic 1 information and applies to a spatial model slightly different from ours. Query languages are not considered in [KPV95] Various notions of G genericity for different groups G of permutations are discussed in [Par 94] A spatial database model ....

....use of these results. Closest to our topological invariants is a representation of topological information proposed in [KPV95] which is lossless with respect to isotopy generic 1 information and applies to a spatial model slightly different from ours. Query languages are not considered in [KPV95]. Various notions of G genericity for different groups G of permutations are discussed in [Par 94] A spatial database model that includes spatial and classical database information is proposed, along with a calculus and equivalent algebra. Much of the formal work related to spatial databases ....

[Article contains additional citation context not shown here]

B. Kuijpers, J. Paredaens and J. Van den Bussche. Lossless Representation of Topological Spatial Data. In Proc. Fourth Int'l. Symp. on Large Spatial Databases, 1995.

....of data. The constraint data model, first introduced by Kanellakis, Kuper and Revesz [KKR90] offered a promising paradigm for the representation of all sorts of data in a unified framework. Linear constraints over rational numbers have been shown to fit the need of spatial data in the vector mode [KPV95, GK97]. Spatial objects, seen as infinite sets of points, could be dealt with as first class citizens with an explicit representation. This contrasts with the representation of spatial objects by their boundary in vector mode for instance, which lead to cumbersome data models with ad hoc operations, and ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M. J. Egenhofer and J. R. Herring, editors, Advances in Spatial Databases, 4th Int. Symp., SSD'95, pages 1--13. Springer, 1995.

....This results in an extremely efficient optimization mechanism, very easy to use in practical applications. 1 Introduction The recent field of constraint databases, initiated at the beginning of the decade [KKR90] has lead to sound data models and query languages for multi dimensional data [PVV94,GST94,KG94,KPV95,GK97]. It allows to represent infinite relations of arbitrary dimension by quantifier free formulae over some arithmetical domain, and to manipulate these relations in a symbolic way. There have been many theoretical studies on constraint databases, mostly focused on the Work supported in part by ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M. J. Egenhofer and J. R. Herring, editors, Advances in Spatial Databases, 4th Int. Symp., SSD'95, pages 1--13. Springer, 1995.

....under homeomorphisms. These are particularly relevant to applications such as geographic information systems. It it shown in [PSV96] that topological information about semi algebraic regions can be precisely and naturally described using a finite structure. A similar invariant is exhibited in [KPdB95] for isotopy invariant information. Such a structure acts as an invariant characterizing a class of topologically equivalent spatial instances. It is an abstraction capturing exactly the topological properties of a set of regions. For semi algebraic regions, the invariant can be computed in ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche, Lossless representation of topological spatial data, Fourth Int'l. Symp. on Large Spatial Databases, 1995.

....set S, represented by a labeled plane graph. The labeled plane graph completely captures S: for each point the coordinates are known, and for each line an equation is known. Now suppose a number of applications are only interested in the topology of S. Such applications are practically motivated [TL92, KPVdB95]. Then these applications are not interested in the coordinates and equations. Indeed, if we ignore coordinates and equations, a labeled plane graph only describes the topology of the spatial database. Now a crucial observation is that the abstract labeled plane graph obtained from a concrete ....

....authors showed that two spatial databases represented by two isomorphic canonical labeled plane graphs must be topologically equivalent (in mathematical terms, TOPOLOGICAL CANONIZATION 3 canonization canonization Original data Canonical View update Figure 1. 1 Example of an update isotopic) [KPVdB95]. 1 This implies that a computationally complete query language for topological queries is obtained simply by using any computationally complete query language for classical generic database queries [AHV95] on the canonical labeled plane graph. A second advantage, as argued recently by ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M.J. Egenhofer and J.R. Herring, editors, Advances in Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 1--13. Springer, 1995.

....plane graph. The labeled plane graph completely captures S: for each point the coordinates are known, and for each line an equation is known. Now suppose a number of applications are only interested in the topology of S. Such applications are practically motivated [Thompson and Laurini, 1992, Kuijpers et al. 1995]. Then these applications are not interested in the coordinates and equations. Indeed, if we ignore coordinates and equations, a labeled plane graph only describes the topology of the spatial database. Now a crucial observation is that the abstract labeled plane graph obtained from a concrete ....

....topological property of the original database. More speci cally, Paredaens and two of the present authors showed that two spatial databases represented by two isomorphic canonical labeled plane graphs must be topologically equivalent (in mathematical terms, iso TOPOLOGICAL CANONIZATION 3 topic) [Kuijpers et al. 1995]. 1 This implies that a computationally complete query language for topological queries is obtained simply by using any computationally complete query language for classical generic database queries [Abiteboul et al. 1995] on the canonical labeled plane graph. A second advantage, as argued ....

Kuijpers, B., Paredaens, J., and Van den Bussche, J. (1995). Lossless representation of topological spatial data. In Egenhofer, M. and Herring, J., editors, Advances in Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 1-13. Springer.

....will be regular. From a purely topological point of view, the simpli cation of a graph contains in a compact manner the same information as the original graph. Such lossless topological representations (also called topological invariants ) have recently been studied by a number of researchers [3, 6, 7]. For example, initial experiments reported on by Segou n and Vianu have shown drastic compression 2 of the size of the data by topological simpli cation. Of course, if we want to answer path queries using the simpli ed graph instead of the original one, we are faced with the problem of on line ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M.J. Egenhofer and J.R. Herring, editors, Advances in Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 1-13. Springer, 1995.

....this representation of a database is invariant . Figure 5 gives a database in the topological data model that gives rise to the same instances for R 1 ; R 2 ; R 3 and R 4 as the one of Figure 4. This shows that this representation is not lossless. Kuijpers, Paredaens and Van den Bussche give in [29] a representation of databases in the topological data model that is both invariant and lossless. The notion of an observation of a database from one of its labeled points is at the basis of this representation. For each labeled point in a spatial database, we make a circular alternating list of ....

....of the point. This is illustrated in Fig. 6. There, the alternating list for the point with name p is (ff B ff A fi C fi A) A point which is isolated from the remainder of the database gives rise to an observation consisting of one single area label. We denote the observation from p by Obs(p) In [29] it is shown that the concept of observation is well defined. Clearly, also a representation of a database by means of observations is invariant. The examples of Figure 5 again show that observations alone are not enough to achieve losslessness. In [29] Definition 6 For a given database D, we ....

[Article contains additional citation context not shown here]

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In Egenhofer and Herring [16].

.... Pi 123 (R 3 ) Pi 312 (R 4 ) and (ffpAi) 2 R 3 (ffqB) 2 Pi 123 (R 3 ) ApQ) 2 R 1 9 = ffqBi 1) 2 R 3 : ut It is more convenient to denote the relation R 4 of Example 5 for each labeled point p as a circular alternating list of curve and area labels rather than as a set of tuples [19]. Actually, this alternating list of labels corresponds to the labels of the curves and areas that an observer, placed in the point p, sees when he makes a full clockwise circular scan of the environment of the point p. A formal definition of this alternating circular list was given in [19] and it ....

....tuples [19] Actually, this alternating list of labels corresponds to the labels of the curves and areas that an observer, placed in the point p, sees when he makes a full clockwise circular scan of the environment of the point p. A formal definition of this alternating circular list was given in [19] and it was referred to as the observation of a spatial database from the point p and denoted as Obs(p) The collection of the observations of a spatial database from each of its points is called the observation of the spatial database. The observation of a spatial database satisfies the first ....

[Article contains additional citation context not shown here]

B. Kuijpers, J. Paredaens, and J. Van den Bussche "Lossless representation of topological spatial data," in Proceedings 4th Symposium on Advances in Spatial Databases, M. J. Egenhofer and J. R. Herring, eds., Lecture Notes in Computer Science, vol. 951. Springer Verlag, Berlin, 1995, 1--13.

....Isotopic means homeomorphic by an orientation preserving homeomorphism. p Gamma 2 p 4 (a) b) l 3 l 4 p 2 p 4 p 1 p 3 l 1 l Gamma 1 p 1 p 3 l 2 a 2 a Gamma 2 a Gamma 1 a 1 Figure 3: A frame of a movie X (a) and its graph GX (b) From results in [10] it follows that A and B are isotopic if and only if there exist bijections b P : PA PB , b L : LA LB , and b A : AA AB that map labels to labels and Gamma labels to Gamma labels and that preserve the clockwise occurrence of edges and areas around each of the labeled nodes. ....

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless Representation of Topological Spatial Data. In M. Egenhofer and J. Herring, editors, Advances in Spatial Databases, 4th International Symposium, SSD'95, volume 951 of Lecture Notes in Computer Science, pages 1--13, Springer-Verlag, 1995.

No context found.

Kuijpers, Bart, Paradaens, Jan, and van den Bussche, Jan (1995). Lossless representation of topological spatial data. In Egenhofer, M.J. and Herring, J.R., editors, Proceedings, 4th International Symposium on Large Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 1-13, Berlin. Springer.

No context found.

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In Advances in Spatial Databases (SSD'95), volume 951 of Lecture Notes in Computer Science, pages 1-13. Springer-Verlag, 1995.

No context found.

B. Kuijpers, J. Paredaens, and J. Van den Bussche. Lossless representation of topological spatial data. In M.J. Egenhofer and J.R. Herring, editors, Advances in Spatial Databases, volume 951 of Lecture Notes in Computer Science, pages 1--13. Springer, 1995.

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