J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of 13th ACM Symposium on Principles of Database Systems, Minneapolis, Minnesota, pages 279--288, May 1994. 33  Home/Search   Document Not in Database   Summary   Related Articles   Check

....integrity constraints, spatiotemporal databases. 1 Introduction Constraint databases [KKR95] generalize in a natural way the relational model of data by allowing in nite relations that are nitely representable using constraints. Constraint databases nd numerous applications in spatial [BJM93, BK95, BLLM95, PVdBVG94, VGVG95], temporal [Cho94, Tom97] and spatiotemporal databases [GRS98a, GRS99] A variety of constraint languages have been proposed, including dense order constraints, linear arithmetic constraints and the most general polynomial constraints [GK96, BDLW98] The fundamental relational query languages, ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a Theory of Spatial Database Queries. In ACM Symposium on Principles of Database Systems, pages 279-288, Minneapolis, Minnesota, 1994.

....write (S, 3ip) to denote the induced substructure of (L, 3ip) with universe S. 3.2 Finding an Adequate Notion of Genericity When dealing with (L, databases that live in a context structure (L, 3ip) one has to revisit the concept ofgenericity. Paredaens, Van den Bussche, and Van Gucht [25] (see also [20] pointed out that the adequate notion of genericity depends on the particular context (or, the geometry) in which the information stored in a database is interpreted. For the particular context considered in the present paper, this can be explained as follows: Recall that the ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In PODS'94: 13th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 279 288. ACM Press, 1994. 69

....databases, aggregation, closure, integrity constraints. 1 Introduction Constraint databases [KKR95] generalize in a natural way the relational model of data by allowing in nite relations that are nitely representable using constraints. Constraint databases nd numerous applications in spatial [BJM93, BK95, BLLM95, PVdBVG94, VGVG95], temporal [Cho94, Tom97] and spatiotemporal databases [GRS98a, GRS99] A variety of constraint languages have been proposed, including dense order constraints, linear arithmetic constraints and the most general polynomial constraints [GK96, BDLW98] The fundamental relational query languages, ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a Theory of Spatial Database Queries. In ACM Symposium on Principles of Database Systems, pages 279-288, Minneapolis, Minnesota, 1994.

....in MuTACLP a notion of time unit and a set of conversion predicates which transform time points into the chosen time unit (see, e.g. 4] We nally observe that in MuTACLP also spatial data can be naturally modelled. In fact, in the style of the constraint databases approaches (see, e.g. [24, 36, 19]) spatial data can be represented by using constraints. The facilities to handle time o ered by MuTACLP allows one to easily establish spatio temporal correlations, for instance time varying areas, or, more generally, moving objects, supporting either discrete or continuous changes (see [37, 30, ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of the 13th ACM Symposium on Principles of Database Systems, pages 279-288, 1994.

....A 1 , i.e. r(v) v 1 . A certain class of regularity shaped regions can be represented nitely by means of semi algebraic formulas. The representation of spatial objects by a nite number of attributes A 1 ; An where A i ranges over semi algebraic formulas was discussed, for example, by Paredaens, Van den Bussche Van Gucht (1994). 5.3 De nite Fiats forming Regional Partitions Let (A 1 ; An ) fo 1 ; o m g be a set of de nite at objects. Every object o i 2 (A 1 ; An ) is characterized by a attribute n tuple (a 1 ; an ) Assume the regions of the objects o 1 ; o m sum up the ....

Paredaens, J., Van den Bussche, J. & Van Gucht, D. (1994), Towards a theory of spatial database queries, in `Thirteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems', Minneapolis.

.... set constraints (Revesz, 1995) dense order constraints (Grumbach and Su, 1995) Linear constraints over reals drew special attention (Afrati et al. 1994, Brodsky and Kornatzky, 1995, Tollu et al. 1995, Vandeurzen et al. 1995) The use of constraints in spatial databases was addressed in (Paredaens et al. 1994), and to describe incomplete information in (Srivastava et al. 1994) constraint aggregation was studied in (Kuper, 1993) The remainder of the paper is organized as follows. Motivating examples and discussion are next, in Section 2, and the definitions of our data model and query language ....

Paredaens, J., Van den Bussche, J. & Van Gucht, D. (1994). Towards a theory of spatial database queries. In Proc. ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 1994.

....sequentiality, for example. A logical interpretation of the primitives is described, and algorithms to create and traverse this representation are given. There is relatively little theoretical work on multimedia databases. Some initial work on databases for geometrical information is presented in [36]. The paper tries to adapt the basic theoretical concept of genericity of relational databases to the case where data does have some intrinsic semantics attached to it (geometrical, in this case) summary: ffl modeling of time based media [22] ffl video information contents and film theory ....

.... where data does have some intrinsic semantics attached to it (geometrical, in this case) summary: ffl modeling of time based media [22] ffl video information contents and film theory [26] ffl interval based models for time dependent multimedia data [32] ffl theory of spatial database queries [36] 3 3 Content based retrieval Access structures which support efficient content based retrieval of multimedia objects, form one of the most important parts of multimedia information management systems. One important stream of research effort in developing indexing structures for spatial and ....

Paredaens, J., Van den Bussche, J., and Van Gucht, D., Towards a Theory of Spatial Database Queries. Proceedings of ACM PODS'94 , ACM Symposium on Principles of Database Systems, Minneapolis, Minnesota, USA, May 1994, pp. 279--288.

....69978, Israel, milo math.tau.ac.il x Department of Computer Science, The Hebrew University, Jerusalem 91904, Israel, paula cs.huji.ac.il model, the data types used in instances of a data model, and queries. Several recent papers have indicated the role of having different notions of genericity [9, 13]. On a more pragmatic level, genericity can be used as a tool for proving inexpressibility results: If one shows that all queries in a language are of a certain genericity class, then queries not in the class are not expressible. We follow Chandra [6] in presenting a few such results. Also, we ....

J. Paredaens, J. V. den Bussche, and D. V. Gucht. Towards a theory of spatial database queries. In PODS, pages 279 -- 288, 1994.

....is invariance under some class of mappings [BMT96] The larger this class of mappings, the smaller resulting class of queries. The class can be defined by a set of constants and functions that need to be preserved, or by some other means. For example, in recent work on spatial query languages [PVV94, PSV96], genericity is considered w.r.t. translations, similarities and homeomorphisms of the plane, and each defines a different class of queries. In [BMT96] we defined the class of fully generic queries as those queries that are invariant under the largest class of mappings. Being the smallest ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In ACM Symposium on Principles of Database Systems, pages 279 -- 288, 1994.

.... sets so defined are called semilinear; for hR; 0; 1; i they are called semi algebraic, cf. 42] The query languages for constraint databases are the same as those we considered for finite ones: FO(SC; Omega Gamma4 2 Without loss of generality, we do not assume relational attributes, as in [13, 27] and some other papers. They do not affect our results, but would make notation heavier. 20 If M = hU ; Omega i is an infinite structure, let Obj( Omega Gamma be the class of finitely representable databases over M, that is, Obj( Omega Gamma = S n Obj n( Omega Gamma and Obj n( Omega Gamma ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In PODS'94, pages 279--288.

....a way. The model M is typically chosen to admit quantifier elimination. Then the query evaluation process reduces to application of the quantifier elimination procedure [20] Recently, attention has shifted from finitely represented models (that is, those that arise as M ) to finite ones, cf. [4, 21, 23, 24]. Since queries arising in geographical applications often involve regions that are determined by a fixed finite number of points (i.e. a convex polygon can be given by its vertices) we can convert most interesting questions involving finitelyrepresented models to questions involving finite ....

....be given by its vertices) we can convert most interesting questions involving finitelyrepresented models to questions involving finite models [22] For example, it was conjectured that first order logic with polynomial inequality constraints cannot express topological connectivity. A result of [23] reduced that problem to connectivity of finite graphs whose nodes come from R, and the problem for graph connectivity was recently solved in [4] In addition, the setting of finite databases embedded in a fixed infinite structure enables one to study constraint databases via the tools of finite ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In PODS'94, pages 279--288.

.... Poly or FO Lin The first reaction is to say no . Indeed, it is well known that over finite structures, FO cannot define graph connectivity (see, e.g. 14] and topological connectivity appears to be a natural continuous analog of graph 4 connectivity. This intuition was made precise in [29] where it was shown that if FO Poly defines topological connectivity of semi algebraic sets, then it defines graph connectivity of finite graphs. The idea of the reduction is to embed a finite graph G into R 3 without self intersections. This reduces the problem of topological connectivity ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In PODS'94, pages 279--288.

.... of the Fund for Scienti c Research of Flanders (FWO Vlaanderen) 1 Introduction The framework of constraint databases, introduced by Kanellakis, Kuper and Revesz [10] an overview of the area of constraint databases can be found in [14] provides a rather general model for spatial databases [16]. In this context, a spatial database, which conceptually can be viewed as an in nite set of points in the real space, is nitely represented as a union of systems of polynomial equations and inequalities (in mathematical terminology, such gures are called semi algebraic sets [3] The set of ....

....(GIS) 0,0) Fig. 1. An example of a spatial database. In the past ten years, several languages to query spatial databases have been proposed and studied. A very natural query language, commonly known as FO Poly, is obtained by extending the relational calculus with polynomial inequalities [16]. The query that returns the topological interior of a database S is expressed by the FO Poly formula (9 0) 8x 0 ) 8y 0 ) x x 0 ) 2 (y y 0 ) 2 2 S(x 0 ; y 0 ) with free variables x and y that represent the co ordinates of the points in the result of the query. Although ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of the 13th ACM Symposium on Principles of Database Systems, pages 279-288, ACM Press, New York, 1994.

....notion must be relaxed. Suppose that database elements are ordered, and a query may refer to the ordering. In this case the right notion of genericity is invariance under maps that preserve the order relation. For constraint databases, even more complex notions of genericity have been considered [29]. In this paper we use three notions of genericity for Boolean queries. Let : U Ube a mapping on the domain. Then can be extended to databases over U: DB denotes a database obtained from DB by replacing each occurrence of x 2 adom(DB ) by (x) Definition 2. A Boolean query Q is totally ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of 13th ACM Symposium on Principles of Database Systems, Minneapolis, Minnesota, pages 279--288, May 1994.

....in real algebraic geometry as the semi algebraic sets in R k . This is a very well behaved class of geometrical gures, and a lot is known about their topological and geometrical properties [10, 4] So, it seems very natural to use constraint databases over the reals to represent spatial data [22]. Every spatial datum is then a semi algebraic set, which is symbolically stored as a de ning formula over the reals. More traditional approaches to spatial databases [27, 23] represent spatial data as polyhedral subdivisions of the real space, or using a nite number of spatial abstract ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings 13th ACM Symposium on Principles of Database Systems, pages 279-288. ACM Press, 1994.

....have quantifier elimination. In this case, one performs the query evaluation process by applying the quantifier elimination procedure; see [21] The results here give bounds on expressibility in constraint database models based on a wide class of interpreted structures. They extend the results of [5, 25, 26] to show that queries such as parity and graph connectivity cannot be expressed in constraint databases based on any structure lacking the independence property. For structures that are based on the reals, one can then use the techniques of [13] to derive that various topological properties cannot ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In PODS'94, pages 279--288.

....spheres, etc. In [23] Meo et al. proposed adding an association rule operator to SQL. Again, our proposed 3W model is far more general and fundamental. The dimension algebra developed here is related to constraint query languages in general [19, 7] and geometric query languages in particular [26, 13]. Paredaens et al. 26] and Gyssens et al. 13] consider constraint languages that are in the FO[R] class, i.e. first order logic augmented with polynomial inequalities over reals, and relation variables with fixed arities. This class of constraints are shown to have nice properties, such as ....

....Meo et al. proposed adding an association rule operator to SQL. Again, our proposed 3W model is far more general and fundamental. The dimension algebra developed here is related to constraint query languages in general [19, 7] and geometric query languages in particular [26, 13] Paredaens et al. [26], and Gyssens et al. 13] consider constraint languages that are in the FO[R] class, i.e. first order logic augmented with polynomial inequalities over reals, and relation variables with fixed arities. This class of constraints are shown to have nice properties, such as decidability for ....

J. Paradaens, J. Van dn Bussche, and D. Van Gucht. Towards a Theory of Spatial Database Queries. In Proc. 1994 PODS, pp. 279--288.

....testing whether a set of points forms a convex hull. So the coupling of relational calculus with arithmetic constraints enhances power. A natural question, which attracted much attention recently, arises: How much more power can we gain from this coupling In particular, several recent papers [17, 18, 16, 26, 11, 23] made and attempted to settle the following conjecture. Conjecture. Queries such as transitive closure, connectivity test, parity test are not definable in the relational calculus plus polynomial inequality constraints over the reals. These three queries are singled out because they involve two ....

....of data has no effect on the answers to queries. This is usually captured by a notion of genericity. The most standard notion of genericity states that queries are invariant under arbitrary permutations of the domain [1] For constraint databases, more complex notions of genericity were considered [23]. Here we use three notions of genericity. If : U U is an endomap on the domain, then can be extended to databases over U in an obvious way. We use DB to denote this extension. Definition 2 ffl A query Q is totally generic (TG) with respect to a domain U if for any database DB and any ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of 13th ACM Symposium on Principles of Database Systems, Minneapolis, Minnesota, pages 279--288, May 1994.

.... databases (also called constraint databases) where the relations are no longer finite but finitely represented [KLP99] The notion of genericity (invariance of queries under isomorphisms) fundamental for the relational database model, can be generalized to spatial databases in various ways [PVV94]. Given a group G of transformations (translations, affinities, isometries, similarities, homeomorphisms, etc. a query Q is G generic if for all database instances I and each transformation g 2 G, Q(g(I) g(Q(I) By FOG we denote the set of G generic firstorder queries. The genericity of a ....

....(translations, affinities, isometries, similarities, homeomorphisms, etc. a query Q is G generic if for all database instances I and each transformation g 2 G, Q(g(I) g(Q(I) By FOG we denote the set of G generic firstorder queries. The genericity of a first order query is undecidable [PVV94], but the expressive power of FO G can be understood via sound and complete (decidable) languages. A language is said to be sound for G if it contains only FOG queries. It is complete for G if it expresses all FO G queries. The choice of the group G depends on which information one is interested ....

J. Paredaens, J. Van Den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proc. ACM Symp. on Principles of Database Systems, pages 279--288, 1994.

....a final section of this paper, we look at queries that are generic, i.e. that do not distinguish between isomorphic databases. Genericity is a natural criterion in the context of classical relational databases [2, 10] Perhaps this is a little less so for databases over the reals; in other work [18] we have proposed alternative, spatial genericity criterions based on geometrical intuitions. 4 Nevertheless, it remains interesting to investigate which classically generic queries can be expressed using linear constraint sentences. Sentences that do not contain any polynomial inequalities ....

J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. Proceedings 13th ACM Symposium on Principles of Database Systems, 1994.

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J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a theory of spatial database queries. In Proceedings of 13th ACM Symposium on Principles of Database Systems, Minneapolis, Minnesota, pages 279--288, May 1994. 33

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J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a Theory of Spatial Database Queries. ACM Symposium on Principles of Database Systems, 279--288, Minneapolis, Minnesota, 1994.

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J. Paredaens, J. Van den Bussche and D. Van Gucht. Towards a Theory of Spatial Database Queries. In ACM Symposium on Principles of Database Systems, pp.279-288, 1994

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J. Paredaens, J. Van den Bussche, and D. Van Gucht. Towards a Theory of Spatial Database Queries. In ACM Symposium on Principles of Database Systems, pages 279-288, Minneapolis, Minnesota, 1994.

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J. Paredaens, J. Van den Bussche, and D. Van Gucht. Toward a theory of spatial database queries. In Proc. of the ACM Symposium on Principles of Database Systems, PODS, volume 13, pages 279-288. ACM Press, 1994.

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