Egenhofer, M. and Sharma, J. (1993). Assessing the consistency of complete and incomplete topological information. Geographical Systems 1, pages 47--68.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... are often referred to in the literature as topological inference problems [CGP98a] CGP98b] CHK99] They have proved to be relevant in the area of geographic information systems [E93] EF91] and in graph drawing [DETT99] In spite of many e orts [K91a] K98] and false claims [SP92] [ES93]) no algorithm was found for their solution. It is known that these problems are at least NP hard [KM89] K91b] MP93] Since each element of a nite system of regions in the plane can be replaced by a simple continuous arc ( string ) lying in its interior so that the intersection pattern of ....

M. Egenhofer and J. Sharma, Assessing the consistency of complete and incomplete topological information, Geographical Systems 1 (1993), 47-68.

....on the set of regions, and consider only the relational part. Since the calculus handles relations, no knowledge about the concrete geometrical objects is necessary. Relation algebras were introduced into spatial reasoning by Egenhofer Sharma (1992) with additional results published in Egenhofer Sharma (1993), Egenhofer (1994) Many well known spatial relations can be expressed by the relation operators and constants, #, and the single relation C,for example, P # ##C# #C#; part of (1.7) PP # P ##I: proper part of (1.8) O # P## P overlap (1.9) PO# O ###P # P## partially overlap (1.10) EC # C ##O ....

Egenhofer, M. & Sharma, J. (1993). Assessing the consistency of complete and incomplete topological information. Geographical Systems 1, 47--68.

.... objects in the network affects not only the two objects, but the insertion might yield additional constraints between other objects (constraint propagation) Studies of constraint propagation and consistency checking in networks of topological relations can be found in (Smith and Park, 1992) and (Egenhofer and Sharma, 1993). Hernandez, 1993) studied constraint networks of direction and topological relations. Egenhofer and Herring (1990) have developed a system which deals with a modelling space consisting of the binary topological relations disjoint, meet, equal, overlap, contains (and the converse relation inside) ....

Egenhofer, M., Sharma, J. (1993) Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems, Vol 1, pp. 47-68.

....structures bibliography, the term overlap (instead of not disjoint) is used to denote any configuration in which the objects are not disjoint. 3 (Keighan, 1993) Furthermore, the relations of m t2 have been influential in assessing the consistency of topological information in spatial databases (Egenhofer and Sharma, 1993), query optimisation strategies (Clementini et al. 1993) and Spatial Reasoning (Sharma et al. 1994) This paper is concerned with the retrieval of the topological relations of m t2 using spatial data structures based on Minimum Bounding Rectangles (MBRs) In particular we concentrate on R trees ....

....step is needed for all MBR configurations (including those of Figure 12) In order to model linear and point data we need further extensions because the topological relations that can be defined, as well as the number of possible projection relations between MBRs, depend on the type of objects. Egenhofer (1993), for instance, defined 33 relations between lines based on the 9 intersection model, while Papadias and Sellis (1994a) have shown that the number of different projections between a region reference object and a line primary object is 221. The ideas of the paper can be extended to include linear ....

Egenhofer, M., Sharma, J. (1993) Assessing the Consistency of Complete and Incomplete Topological Information.

....very often in geographic space, relations among spatial entities are as important as the entities themselves. Depending on the application domain, some spatial relations may be more significant than others: topological relations have been used to access consistency in Geographical Databases (Egenhofer and Sharma, 1993), ordinal relations to describe aggregation hierarchies (Kainz et al. 1993) and direction relations have been incorporated in Spatial Query Languages (Papadias and Sellis, 1994a) Topological relations describe concepts of neighbourhood, incidence and overlap and stay invariant under ....

....approach on topological relations is based to the 4 intersection model. This model is the prevalent model for topological relations in the literature and has been used in a wide range of applications such as Spatial Reasoning (Sharma et al. 1994) and consistency checking in Geographic Databases (Egenhofer and Sharma, 1993). Furthermore, experimental studies have shown that it has the potential for defining cognitively meaningful spatial predicates, a fact that renders it attractive for user interfaces. We also defined a set of direction relations between extended objects, because the previous sets of direction ....

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Egenhofer, M., Sharma, J. (1993) Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems, Vol 1, pp. 47-68.

....1. INTRODUCTION There has been an increasing interest recently about the representation and processing of spatial relations in Spatial Database Systems (for an extensive discussion see [Papa94c] This interest has focused on several topics such as Reasoning [Fran95] Consistency Checking [Egen93] and Spatial Query Languages [Papa95a] In this paper we deal with the retrieval of spatial relations in DBMSs used for geographic, or more generally, spatial, applications. In particular we concentrate on the retrieval of direction relations using B and R tree based data structures. Direction ....

Egenhofer, M., Sharma, J., "Assessing the Consistency of Complete and Incomplete Topological Information", Geographical Systems, Vol. 1, pp. 47-68, 1993.

.... between two objects in the network affects not only the two objects, but the insertion may yield additional constraints between other objects (constraint propagation) A study of constraint propagation and consistency checking in networks of spatial relations can be found in (Hernandez, 1993) Egenhofer and Sharma (1993) studied consistency checking in constraint networks of topological relations. A B C E D below disjoint meet covers contains disjoint left left Fig. 3 A spatial constraint network Chang et al. 1987) developed the two dimensional string (2D string) representation for encoding symbolic images, ....

Egenhofer, M., Sharma, J. (1993) Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems, vol 1, 47-68.

.... of qualitative inference methods, extending constraint reasoning mechanisms to take the rich structure of physical space into consideration (Hern andez 1992) Related research on topological relations in the context of GIS has been done by Egenhofer (1989, 1991) Egenhofer and Al Taha (1992) Egenhofer and Sharma (1993), and Smith and Park (1992) An alternative definition of topological relations based on the primitive C(x,y) x connects with y (x and y being regions) has been proposed by Cui, Cohn, and Randell (1992) Also relevant for GIS applications are a qualitative algebra for reasoning about distances ....

Egenhofer, M. J. and Sharma, J. (1993). Assessing the consistency of complete and incomplete topological information. Geographical Systems, 1, 47--68.

....a model, a picture of four regions so related; if not, a proof of impossibility. This deceptively simple extension of propositional logic is known as the topological inference problem [5] and its special cases, extensions, and variants are studied in the area of geographic information systems [3, 4, 10, 5, 11]. Despite much effort (and claims in the literature [12, 4] no decision algorithm and finite axiomatization for this problem is known although the problem becomes both finitely axiomatizable and polynomial time decidable in any number of dimensions other than two. In fact, the following ....

....impossibility. This deceptively simple extension of propositional logic is known as the topological inference problem [5] and its special cases, extensions, and variants are studied in the area of geographic information systems [3, 4, 10, 5, 11] Despite much effort (and claims in the literature [12, 4]: no decision algorithm and finite axiomatization for this problem is known although the problem becomes both finitely axiomatizable and polynomial time decidable in any number of dimensions other than two. In fact, the following special Dept. of Math. Sci. Tokyo Denki University, ....

M. J. Egenhofer and Jayant Sharma. Assessing the consistency of complete and incomplete topological information. Geographical Systems, 1:47--68, 1993.

.... relation between two objects in the network a#ects not only the two objects, but the insertion might yield additional constraints between other objects (constraint propagation) Studies of constraint propagation and consistency checking in networks of topological relations can be found in [33] and [9]. Hernandez [16] studied constraint networks of direction and topological relations. Egenhofer and Herring [8] have developed a system which deals with the binary topological relations disjoint, meet, equal, overlap, contains (and the converse relation inside) and covers (and the converse ....

.... composition tables for homogeneous spatial constraints (e.g. topological in [7] direction in [27] and for combinations of several types of constraints (e.g. topological and direction in [16] direction and distance in [10] Path consistency algorithms have a polynomial complexity [33] [9] but in general do not su#ce for achieving satisfiability. They reveal only local inconsistencies, and search based constraint satisfaction algorithms (such as backtracking) have to be applied to locally consistent networks in order to ensure global satisfiability . Although such algorithms have a ....

Egenhofer, M., Sharma, J.: Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems 1, 1993, pp. 47--68.

.... objects in the network affects not only the two objects, but the insertion might yield additional constraints between other objects (constraint propagation) Studies of constraint propagation and consistency checking in networks of topological relations can be found in (Smith and Park, 1992) and (Egenhofer and Sharma, 1993). Hern ndez, 1993) studied constraint networks of direction and topological relations. Egenhofer and Herring (1990) have developed a system which deals with a modelling space consisting of the binary topological relations disjoint, meet, equal, overlap, contains (and the converse relation inside) ....

Egenhofer, M., Sharma, J. (1993) Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems, Vol 1, pp 47-68.

....only on the nature of the constraints; their early detection helps avoid unnecessary extensive access to stored data. In real applications, that involve a large number of constraints imposed by numerous agents, the detection of inconsistencies requires sophisticated spatial inference mechanisms (Egenhofer and Sharma 1993), Grigni, Papadias and Papadimitriou 1995) In case that some inconsistencies have been detected the agents will have to revise their constraints, which is in essence a negotiation process. The nature of this process is highlighted in (Golay 1995) which proposes that distributed cognition can be ....

Egenhofer, M. and J. Sharma (1993) Assessing the Consistency of Complete and Incomplete Topological Information, Geographical Systems 1, pp. 47-68.

....of the other 7 relations. This concrete domain does not allow concrete objects to be associated with concrete polygonal areas (for this additional unary predicates would be needed) Therefore, a standard algorithm for relational consistency and realizability of sets of topological constraints ( [ 5 ] , 6 ] can be used to decide the satisfiability of finite conjunctions of predicates in our concrete domain. Relational consistency and realizability are different problems since there may be models which are relationally consistent but not realizable in the plane. In the case of this simple ....

M. J. Egenhofer and J. Sharma. Assessing the consistency of complete and incomplete topological information. In Geographical Systems, volume 1, pages 47--68, 1993.

.... that describe concepts of neighbourhood and incidence (e.g. overlap, disjoint) 8] and distances (e.g. near, far) 17] The above types of relations have been used in a wide range of topics, such as Spatial Query Languages [12, 26] Reasoning [5, 17] and Consistency Checking Mechanisms [9, 14]. This paper describes implementations of direction relations in Spatial Database Management Systems (SDBMS) and Geographical Information Systems (GIS) Despite the fact that directions constitute an important class of user queries, they have not been studied extensively in spatial access methods. ....

M.J. Egenhofer and J. Sharma, Assessing the Consistency of Complete and Incomplete Topological Information, Geographical Systems, 1 (1993) 47-68.

....one according to the analytical estimate. 17 7. DISCUSSION Work on spatial relations has provided formal definitions (Egenhofer and Franzosa, 1991; Frank, 1996) models of representation and reasoning (Hernandez, 1994; Papadias et al. 1996) algorithms for spatial constraint satisfaction (Egenhofer and Sharma, 1993; Grigni et al. 1995) and specialized query languages (Roussopoulos et al. 1988) The focus of this paper is on n dimensional ranges (n 2) that arise during the processing of relations in spatial applications. We defined a set of relations often found in such applications and we transformed ....

Egenhofer, M.J., Sharma, J. "Assessing the Consistency of Complete and Incomplete Topological Information", Geographical Systems, Vol. 1(1), pp. 47-68, 1993.

.... (Grigni et al. 1995) direction in (Papadias and Sellis, 1994) distance in (Topaloglou, 1994) and for combinations of several types of constraints (topological and direction in (Hernandez, 1994) direction and distance in (Frank, 1992) Path consistency algorithms have a polynomial complexity (Egenhofer and Sharma, 1993) but in general do not suffice for achieving satisfiability. They reveal only local inconsistencies and search based constraint satisfaction algorithms (such as backtracking) have to be applied to locally consistent networks in order to ensure global satisfiability. Although such algorithms have ....

Egenhofer, M., and Sharma, J. (1993), "Assessing the Consistency of Complete and Incomplete Topological Information", Geographical Systems 1/1, 47-68.

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Egenhofer, M. and Sharma, J.: Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems. 1:(1993) 47-68.

....queries in the form of first order predicates or extended SQL statements. Depending on the configuration, fewer binary relations may be sufficient to describe the scene completely if they allow to drive uniquely the eliminated relations through compositions of elementary or inferred relations [20]. There are additional dependencies among the different types of binary relations that could further reduce the smallest number of relations required to fully specify a scene. For example, detailed cardinal directions imply their corresponding coarse cardinal directions. The actual number of ....

M. Egenhofer and J. Sharma, "Assessing the Consistency of Complete and Incomplete Topological Information," Geographical Systems, vol. 1, no. 1, pp. 47-68, 1993.

....containers and surfaces. Algebras over spatial relations provide powerful mechanisms for spatial reasoning [6, 8, 40] Such inferences have become increasingly important in geographic information systems where people record field observations [13, 33] and later analyze them to find new information [7]. Unlike calculations that employ traditional computational geometry, spatialrelation algebras rely on symbolic computations over small sets of relations [3] This method is This work has been partially supported by the National Science Foundation through NSF grants IRI 9309230, IRI9613646, ....

M. Egenhofer and J. Sharma, "Assessing the Consistency of Complete and Incomplete Topological Information," Geographical Systems, vol. 1, no. 1, pp. 47-68, 1993.

.... Databases, and Geographic Information Systems (GIS) created the need to answer queries involving direction (and other spatial) relations (e.g. find all major cities northeast of Boston in New England ) This has motivated a significant amount of research on Reasoning (Smith and Park, 1992; Egenhofer and Sharma, 1993), Query Processing (Clementini et al. 1994; Papadias et al. 1995) and Spatial Query Languages (Roussopoulos et al. 1988; Egenhofer, 1994, Papadias and Sellis, 1995) A number of relation based systems have been proposed for the representation of direction relations. Chang et al. 1987) ....

Egenhofer, M., Sharma, J. "Assessing the Consistency of Complete and Incomplete Topological Information". Geographical Systems, Vol. 1, No 1, pp. 47-68, 1993.

....Information Systems community, spatial reasoning has been used for inference and consistency checking in spatial (or multimedia) databases. Sistla et al. (1994) propose a set of direction relations in 3D space and define a set of rules which is sound and complete. Smith and Park (1992) and Egenhofer and Sharma (1993) provide methods for detecting topological inconsistencies in spatial databases using constraint satisfaction algorithms (a survey of related work which also includes directions can be found in Hernandez 1994) Reasoning techniques have also 3 been applied for spatial query processing ....

Egenhofer, M., Sharma, J. "Assessing the Consistency of Complete and Incomplete Topological Information". Geographical Systems, Vol. 1, No 1, pp. 47-68, 1993.

.... direction in [Papadias et al. 1994] distance in [Topaloglou, 1994] and for combinations of several types of constraints (topological and direction in [Hernandez, 1994] direction and distance in [Frank, 1992] Path consistency algorithms have a polynomial complexity [Smith and Park, 1992] [Egenhofer and Sharma, 1993] but in general do not su#ce for achieving satisfiability. They reveal only local inconsistencies and search based constraint satisfaction algorithms (such as backtracking) have to be applied to locally consistent networks in order to ensure global satisfiability. Although such algorithms have a ....

Egenhofer, M., Sharma, J.: Assessing the Consistency of Complete and Incomplete Topological Information. Geographical Systems, Vol. 1, No 1, pp. 47-68, 1993.

No context found.

Egenhofer, M. and Sharma, J. (1993). Assessing the consistency of complete and incomplete topological information. Geographical Systems 1, pages 47--68.

No context found.

M. J. Egenhofer and Jayant Sharma. Assessing the consistency of complete and incomplete topological information. Geographical Systems, 1:47--68, 1993.

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