L. Segou n and V. Vianu. Querying spatial databases via topological invariants. volume 17, pages 89-98. ACM Press, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....database which represents a complicated database is often called the invariant of the complicated database. Table 1 gives a listing of recent papers in which the lifting method has been used: compl. dbs easy dbs result for result for easy dbs compl. dbs evaluation of evaluation of [29] planar spatial finite dbs fixpoint counting top. FO( dbs queries queries over collapse from collapse from [19] region dbs finite dbs gen.FO( q , x) top. FO( x) to FOadon( to top. FO( over over finitely logical character complexity of [15] representable finite dbs ....

....complexity of [15] representable finite dbs ization of complexity query evaluation dbs classes finitely natural generic natural generic [5] representable finite dbs collapse over collapse over dbs (1 , 3ip (1 , Table 1: Some papers that use the lifting method. Segoufin and Vianu [29] represent a spatial database (of a certain kind) by a finite database called the topological invariant of the spatial database. They concentrate on the evaluation of topological FO( queries against spatial databases over . One of their results is that a topological query against the spatial ....

L. Segoufin and V. Vianu. Querying spatial databases via topological invadants. Journal of Computer and Systems Sciences, 61(2):270 301, 2000.

....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 Segoufin and Vianu [SV98], is that the canonical labeled plane graph is often much smaller than the original labeled plane graph, since all redundancies have been removed. Motivated by these advantages, in the present paper, we consider the scenario where, along with the original spatial database, a canonical view is ....

L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proceedings 17th ACM Symposium on Principles of Database Systems, pages 89--98. ACM Press, 1998.

....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 component) The big challenge introduced by the ....

....induced by the FOL data model, a finite structure which is an abstraction that captures all the topological properties of the spatial database. The strategy of maintaining such a finite structure (from now on called topological invariant) is very useful and has been addressed in the literature [7, 8, 19, 23]. Different abstractions of topological properties have been considered, and each of them can be viewed as an augmentation of the model proposed by the U.S. Census Bureau, which contains topological properties on points, lines and areas [6, 20] Different classes of continuous topological ....

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L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proc. of the ACM Symposium on Principles of Database Systems, PODS, volume 17, pages 89--98. ACM Press, 1998.

.... 1) Remark Note that the bound of Theorem 4 holds for f.r. instances if querying is done via finite codings whose size is at most polynomial in the size of the finite representation. Such codings are known; see, e.g. 7, 30] several papers studied querying via such finite codings [35, 7, 38]. Note also that the method of Theorem 4 can only be applied as top level aggregation, as the result is not guaranteed to be semi algebraic. 7 Conclusions This paper has dealt with the key question of how to add aggregation to constraint query languages. The first fundamental question is whether ....

L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In PODS'98, pages 89--98.

....distance functions with the Euclidean construction based query languages, developing appropriate query languages for fixpoint queries remain as an interesting issue. It is unclear how EuAlg can be extended to capture fixpoint queries, as it was done for FO lin [GK97] and for topological queries [SV98]. Finally, while the restriction to Euclidean geometry is motivated by the importance of the distance function in many spatial applications, it remains a natural question to ask whether the current approach can be adapted to more general objects. The most obvious such extension would be to allow ....

L. Segoufin and V. Vianu. Querying Spatial Databases via Topological Invariants Proc. ACM Symp. on PODS, 89--98, 1998.

.... languages were given for linear constraints [16, 21] Besides, this approach can only work for those queries applied as top level operators (i.e. outputs cannot be reused by other queries) There exists extensive literature on rst order de nable topological properties of constraint databases [28, 22, 24, 33] and it is well known that connectivity and reachability are not rst order [4] Our results on application to hybrid systems are directly inspired by [26, 27] Organization We introduce notations in Section 2. In Section 3, we deal with closure under topological properties. We rst prove a ....

....nable in L PATH . More precisely, the topological invariant of semi linear instances is de nable in L PATH (Lin) and the topological invariant of semi algebraic instances is de nable in L PATH (Poly) Proof : We brie y recall the de nition of topological invariant. The reader is referred to [28, 33] for a more precise description. Given a spatial instance D over a database schema Reg containing only binary relations, a cell partition of D is a partition of R into nitely many connected subsets called cells such that each relation of D is a ( nite) union of cells. The topological ....

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L. Segou n and V. Vianu. Querying spatial databases via topological invariants. JCSS, 61 (2000), 270-301.

....various applications of spatial databases. For example, in geographical databases, queries like Is region A adjacent to region B , Is there a road from A to B , or Is A an island come up very naturally. Therefore, topological queries have received a lot of attention in the literature (e.g. [KPV97, PSV99, SV98, KV99]) A basic result known about topological queries is that connectivity of a region is not expressible in first order logic [GS99, GS97, BDLW96] Thinking of geographical databases again, planar (or 2dimensional) database instances, where all relations are embedded in the plane R 2 , are of ....

....database instances, where all relations are embedded in the plane R 2 , are of particular importance. In [PSV99] it has been proven that all topological properties of a planar spatial database can be represented in a finite structure called the topological invariant of the instance. In [SV98] it has been shown how this topological invariant can be used to answer topological queries. In particular, SV98] have proven that first order topological queries on a spatial database can be automatically translated into fixpoint queries on the topological invariant. The translation of ....

[Article contains additional citation context not shown here]

L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proc. ACM Symp. on Principles of Database Systems, 1998.

....various applications of spatial databases. For example, in geographical databases, queries like Is region A adjacent to region B , Is there a road from A to B , or Is A an island come up very naturally. Therefore, topological queries have received a lot of attention in the literature (e.g. [KPV97, PSV99, SV98, KV99]) A basic result known about topological queries is that connectivity of a region is not expressible in first order logic [GS99, GS97, BDLW96] Thinking of geographical databases again, planar (or 2dimensional) database instances, where all relations are embedded in the plane R 2 , are of ....

....database instances, where all relations are embedded in the plane R 2 , are of particular importance. In [PSV99] it has been proven that all topological properties of a planar spatial database can be represented in a finite structure called the topological invariant of the instance. In [SV98] it has been shown how this topological invariant can be used to answer topological queries. In particular, SV98] have proven that first order topological queries on a spatial database can be automatically translated into fixpoint queries on the topological invariant. The translation of ....

[Article contains additional citation context not shown here]

L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proc. ACM Symp. on Principles of Database Systems, 1998.

.... language was given for linear constraints [15] Besides, this approach can only work for those queries applied as top level operators (i.e. outputs cannot be reused by other queries) There exists extensive literature on first order definable topological properties of constraint databases [26, 20, 22, 30] and it is well known that connectivity and reachability are not first order [4] Our results on application to hybrid systems are directly inspired by [24, 25] Organization We introduce notations in Section 2. In Section 3, we deal with closure under topological properties. We first prove a ....

L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In PODS'98, pages 89--98.

.... language was given for linear constraints [15] Besides, this approach can only work for those queries applied as top level operators (i.e. outputs cannot be reused by other queries) There exists extensive literature on first order definable topological properties of constraint databases [26, 20, 22, 31] which connectivity and reachability are not first order. Our results on application to hybrid systems are directly inspired by [24, 25] Organization We introduce notations in Section 2. In Section 3, we deal with closure under topological properties. We first prove a number of general ....

L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In PODS'98, pages 89--98.

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L. Segou n and V. Vianu. Querying spatial databases via topological invariants. volume 17, pages 89-98. ACM Press, 1998.

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L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In PODS'98, pages 89--98.

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L. Segoufin and V. Vianu. Querying spatial databases via topological invariants. In Proceedings 17th ACM Symposium on Principles of Database Systems. ACM Press, 1998. To appear.

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