The Implementation of the Cell Tree: Design Alternatives and Performance Evaluation

The cell tree is a new dynamic object-oriented index structure for geometric databases. All data objects in the database are represented as unions of convex point sets (cells). The cell tree is a balanced tree structure whose leafs contain the cells and whose interior nodes correspond to a hierarchy of nested convex polyhedra. This index structure allows quick access to the cells (and therefore to the data objects) that occupy a given location in space. Furthermore, the cell tree is designed for paged secondary memory to minimize the number of disk accesses occuring during a tree search. Point locations and range searches can therefore be carried out very efficiently using the cell tree. This paper reports our experiences with the implementation of the cell tree and presents the results of a performance evaluation.

[1]  Hans-Peter Kriegel,et al.  Multidimensional Order Preserving Linear Hashing with Partial Expansions , 1986, ICDT.

[2]  Antonin Guttman,et al.  R-trees: a dynamic index structure for spatial searching , 1984, SIGMOD '84.

[3]  J. T. Robinson,et al.  The K-D-B-tree: a search structure for large multidimensional dynamic indexes , 1981, SIGMOD '81.

[4]  Douglas Comer,et al.  Ubiquitous B-Tree , 1979, CSUR.

[5]  Henry Fuchs,et al.  On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[6]  Klaus H. Hinrichs,et al.  Storage and Access Structures for Geometric Data Bases , 1985, FODO.

[7]  Eugene Wong,et al.  A Dual Space Representation for Geometric Data , 1987, VLDB.

[8]  Christos Faloutsos,et al.  Analysis of object oriented spatial access methods , 1987, SIGMOD '87.

[9]  Hans-Werner Six,et al.  Hintergrundspeicherstrukturen für ausgedehnte Objekte , 1986, GI Jahrestagung.

[10]  Diane Greene,et al.  An implementation and performance analysis of spatial data access methods , 1989, [1989] Proceedings. Fifth International Conference on Data Engineering.

[11]  Jürg Nievergelt,et al.  The Grid File: An Adaptable, Symmetric Multikey File Structure , 1984, TODS.

[12]  Michael Stonebraker,et al.  The design of POSTGRES , 1986, SIGMOD '86.

[13]  Henry Fuchs,et al.  Near real-time shaded display of rigid objects , 1983, SIGGRAPH.

[14]  Klaus Hinrichs,et al.  The grid file system , 1985 .

[15]  E. Wong,et al.  Convex polyhedral chains: a representation for geometric data , 1989 .

[16]  David E. Muller,et al.  Finding the Intersection of n Half-Spaces in Time O(n log n) , 1979, Theor. Comput. Sci..

[17]  Christos Faloutsos,et al.  The R+-Tree: A Dynamic Index for Multi-Dimensional Objects , 1987, VLDB.

[18]  H. Whitney.  Geometric Integration Theory , 1957 .

[19]  Michael Stonebraker,et al.  An Analysis of Rule Indexing Implementations in Data Base Systems , 1986, Expert Database Conf..

[20]  Oliver Günther,et al.  The design of the cell tree: an object-oriented index structure for geometric databases , 1989, [1989] Proceedings. Fifth International Conference on Data Engineering.

[21]  D. T. Lee,et al.  Computational Geometry—A Survey , 1984, IEEE Transactions on Computers.

[22]  Eugene Wong,et al.  A dual approach to detect polyhedral intersections in arbitrary dimensions , 1991, BIT.

[23]  Oliver Günther,et al.  Efficient Structures for Geometric Data Management , 1988, Lecture Notes in Computer Science.

[24]  Reijo Sulonen,et al.  The EXCELL Method for Efficient Geometric Access to Data , 1982, DAC 1982.

[25]  Nick Roussopoulos,et al.  Direct spatial search on pictorial databases using packed R-trees , 1985, SIGMOD Conference.