Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
A population analysis for hierarchical data structures
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Efficient structures for geometric data management
Efficient structures for geometric data management
Redundancy in spatial databases
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
7+&barbelow;2 criteria for assessing and comparing spatial data structures
SSD '90 Proceedings of the first symposium on Design and implementation of large spatial databases
The R*-tree: an efficient and robust access method for points and rectangles
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
Indexing for data models with constraints and classes (extended abstract)
PODS '93 Proceedings of the twelfth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Separability of polyhedra for optimal filtering of spatial and constraint data
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Storing a collection of polygons using quadtrees
ACM Transactions on Graphics (TOG)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Direct spatial search on pictorial databases using packed R-trees
SIGMOD '85 Proceedings of the 1985 ACM SIGMOD international conference on Management of data
Multidimensional binary search trees used for associative searching
Communications of the ACM
The K-D-B-tree: a search structure for large multidimensional dynamic indexes
SIGMOD '81 Proceedings of the 1981 ACM SIGMOD international conference on Management of data
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
The R+-Tree: A Dynamic Index for Multi-Dimensional Objects
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Toward Practical Constraint Databases
VLDB '93 Proceedings of the 19th International Conference on Very Large Data Bases
Proceedings of the Sixth International Conference on Data Engineering
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The filtering method considered in this paper is based on approximation of a spatial object in d-dimensional space by the minimal convex polyhedron that encloses the object and whose facets are normal to preselected axes. These axes are not necessarily the standard coordinate axes; furthermore, their number is not determined by the dimension of the space. We optimize filtering by selecting optimal such axes based on a preprocessing analysis of stored objects or a sample thereof. The number of axes selected represents a trade-off between access time and storage overhead, as more axes usually lead to better filtering but require more overhead to store the associated access structures. We address the problem of minimizing the number of axes required to achieve a predefined quality of filtering and the reverse problem of optimizing the quality of filtering when the number of axes is fixed. In both cases we also show how to find an optimal collection of axes. To solve these problems, we introduce and study the key notion of separability classification, which is a general tool potentially useful in many applications of a computational geometry flavor. The approach is best suited to applications in which the spatial data is relatively static, some directions are more dominant than others, and the dimension of the space is not high; maps are a prime example.