Separability of polyhedra for optimal filtering of spatial and constraint data

Brodsky, Alexander; Lassez, Catherine; Lassez, Jean-Louis; Maher, Michael J.

doi:10.1145/212433.212449

Cited by 26 publications

(11 citation statements)

References 29 publications

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“…To overcome the problem of poor filtering, Brodsky et al [1995] proposed methods for effectively computing a set of optimal axes for separating polyhedra. This work continues the line of work by Jagadish [1990c] in the use of nonstandard axes for better filtering.…”

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confidence: 99%

Multidimensional access methods

1998

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Search operations in databases require special support at the physical level. This is true for conventional databases as well as spatial databases, where typical search operations include the point query (find all objects that contain a given search point) and the region query (find all objects that overlap a given search region). More than ten years of spatial database research have resulted in a great variety of multidimensional access methods to support such operations. We give an overview of that work. After a brief survey of spatial data management in general, we first present the class of point access methods, which are used to search sets of points in two or more dimensions. The second part of the paper is devoted to spatial access methods to handle extended objects, such as rectangles or polyhedra. We conclude with a discussion of theoretical and experimental results concerning the relative performance of various approaches.

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confidence: 99%

Multidimensional access methods

1998

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“…These representations adaptations of the strip tree [Ballard 1981] and the Douglas-Peucker generalization algorithm [Douglas 1990;Douglas and Peucker 1973;Saalfeld 1987] for curves in two dimensions. The number of sides as well as the number of their possible orientations may be expanded so that it is arbitrary (e.g., a convex hull [Brinkhoff et al 1994]), or bounded although greater than the dimensionality of the underlying space (e.g., the P-tree [Jagadish 1990b] and k-DOP [Klosowski et al 1998] where the number of possible orientations is bounded, and the minimum bounding polybox [Brodsky et al 1995], which attempts to find the optimal orientations). The most general solution is the convex hull, which is often approximated by a minimum bounding polygon of a fixed number of sides having either an arbitrary orientation (e.g., the minimum bounding n-corner [Dori and Ben-Bassat 1983;Schiwietz H. Samet 1993;Schiwietz and Kriegel 1993]) or a fixed orientation usually parallel to the coordinate axes (e.g., [Esperança and Samet 1997]).…”

Section: Unit-size Cellsmentioning

confidence: 99%

Object-based and image-based object representations

Samet

2004

ACM Comput. Surv.

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An overview is presented of object-based and image-based representations of objects by their interiors. The representations are distinguished by the manner in which they can be used to answer two fundamental queries in database applications: (1) Feature query: given an object, determine its constituent cells (i.e., their locations in space). (2) Location query: given a cell (i.e., a location in space), determine the identity of the object (or objects) of which it is a member as well as the remaining constituent cells of the object (or objects). Regardless of the representation that is used, the generation of responses to the feature and location queries is facilitated by building an index (i.e., the result of a sort) either on the objects or on their locations in space, and implementing it using an access structure that correlates the objects with the locations. Assuming the presence of an access structure, implicit (i.e., image-based) representations are described that are good for finding the objects associated with a particular location or cell (i.e., the location query), while requiring that all cells be examined when determining the locations associated with a particular object (i.e., the feature query). In contrast, explicit (i.e., object-based) representations are good for the feature query, while requiring that all objects be examined when trying to respond to the location query. The goal is to be able to answer both types of queries with one representation and without possibly having to examine every cell. Representations are presented that achieve this goal by imposing containment hierarchies on either space (i.e., the cells in the space in which the objects are found), or objects. In the former case, space is aggregated into successively larger-sized chunks (i.e., blocks), while in the latter, objects are aggregated into successively larger groups (in terms of the number of objects that they contain). The former is applicable to image-based interior-based representations of which the space pyramid is an example. The latter is applicable to object-based interior-based representations of which the R-tree is an example. The actual mechanics of many of these representations are demonstrated in the VASCO JAVA applets found at

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“…An interesting approach to determine upper bound approximations has been proposed in [12], to improve the selectivity of filtering. The approach is based on the notion of a minimum bounding polybox.…”

Section: Example 5 Consider the Tree Inmentioning

confidence: 99%

“…These axes are not necessarily the standard coordinate axes and, furthermore, their number is not determined by the dimension of the space. The problem of minimizing the number of axes required to achieve a given quality of filtering, as well as the reverse problem of optimizing the quality of filtering when the number of axes is given, are some important topics [12].…”

Section: Example 5 Consider the Tree Inmentioning

confidence: 99%

A constraint-based approach to shape management in multimedia databases

Bertino

Catania

1998

Multimedia Systems

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Shape management is an important functionality in multimedia databases. Shape information can be used in both image acquisition and image retrieval. Several approaches have been proposed to deal with shape representation and matching. Among them, the data-driven approach supports searches for shapes based on indexing techniques. Unfortunately, efficient data-driven approaches are often defined only for specific types of shape. This is not sufficient in contexts in which arbitrary shapes should be represented.Constraint databases use mathematical theories to finitely represent infinite sets of relational tuples. They have been proved to be very useful in modeling spatial objects. In this paper, we apply constraint-based data models to the problem of shape management in multimedia databases. We first present the constraint model and some constraint languages. Then, we show how constraints can be used to model general shapes. The use of a constraint language as an internal specification and execution language for querying shapes is also discussed. Finally, we show how a constraint database system can be used to efficiently retrieve shapes, retaining the advantages of the already defined approaches.

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Separability of polyhedra for optimal filtering of spatial and constraint data

Cited by 26 publications

References 29 publications

Multidimensional access methods

Multidimensional access methods

Object-based and image-based object representations

A constraint-based approach to shape management in multimedia databases

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