Orthogonal Range Queries in OLAP

We study the problem of pre-computing auxillary information to support on-line range queries for the sum and max functions on a datacube. For a d-dimensional datacube with size n in each dimension, we propose a data structure for range max queries with O((4L) d ) query time and O((12L 2 n 1/L γ(n)) d ) update time where L E {1,…,log n} is a user-controlled parameter and γ(n) is a slow-growing function. (For example, γ(n) < log * n and γ(2 4110 ) = 3.) The data structure uses O((6nγ(n)) d ) storage and can be initialized in time linear to its size. There are three major techniques employed in designing the data structure, namely, a technique for trading query and update times, a technique for trading query time and storage and a technique for extending 1-dimensional data structures to d-dimensional ones. Our techniques are also applicable to range queries over any semi-group and group operation, such as min, sum and count.

[1]  Dan E. Willard,et al.  New Data Structures for Orthogonal Queries. , 1979 .

[2]  Jehoshua Bruck,et al.  Partial-Sum Queries in OLAP Data Cubes Using Covering Codes , 1998, IEEE Trans. Computers.

[3]  George S. Lueker,et al.  Adding range restriction capability to dynamic data structures , 1985, JACM.

[4]  Sunita Sarawagi,et al.  Modeling multidimensional databases , 1997, Proceedings 13th International Conference on Data Engineering.

[5]  Michael Ian Shamos,et al.  A Problem in Multivariate Statistics: Algorithm, Data Structure and Applications. , 1978 .

[6]  David Wai-Lok Cheung,et al.  DROLAP - A Dense-Region Based Approach to On-Line Analytical Processing , 1999, DEXA.

[7]  Bernard Chazelle,et al.  Lower bounds for orthogonal range searching: part II. The arithmetic model , 1990, JACM.

[8]  Yannis E. Ioannidis,et al.  Hierarchical Prefix Cubes for Range-Sum Queries , 1999, VLDB.

[9]  Bernard Chazelle.  Filtering Search: A New Approach to Query-Answering , 1983, FOCS.

[10]  Michael L. Fredman,et al.  A Lower Bound on the Complexity of Orthogonal Range Queries , 1981, JACM.

[11]  Nimrod Megiddo,et al.  Range queries in OLAP data cubes , 1997, SIGMOD '97.

[12]  Hermann A. Maurer,et al.  Efficient worst-case data structures for range searching , 1978, Acta Informatica.

[13]  Robert E. Tarjan,et al.  Fast Algorithms for Finding Nearest Common Ancestors , 1984, SIAM J. Comput..

[14]  Jean Vuillemin,et al.  A unifying look at data structures , 1980, CACM.

[15]  Bernard Chazelle,et al.  A Functional Approach to Data Structures and Its Use in Multidimensional Searching , 1988, SIAM J. Comput..

[16]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[17]  Andrew Chi-Chih Yao.  On the Complexity of Maintaining Partial Sums , 1985, SIAM J. Comput..

[18]  Terence R. Smith,et al.  Relative prefix sums: an efficient approach for querying dynamic OLAP data cubes , 1999, Proceedings 15th International Conference on Data Engineering (Cat. No.99CB36337).

[19]  Ambuj K. Singh,et al.  Efficient Dynamic Range Searching Using Data Replication , 1998, Inf. Process. Lett..

[20]  Bernard Chazelle,et al.  Lower bounds for orthogonal range searching: I. The reporting case , 1990, JACM.

[21]  N. Megiddo,et al.  Techniques for Speeding up Range-Max Queries in OLAP Data Cubes , 1997 .

[22]  Azad Bolour.  Optimal Retrieval Algorithms for Small Region Queries , 1981, SIAM J. Comput..

[23]  Jon Louis Bentley,et al.  Multidimensional divide-and-conquer , 1980, CACM.

[24]  Bernard Chazelle,et al.  Computing partial sums in multidimensional arrays , 1989, SCG '89.

[25]  Dan E. Willard,et al.  New Data Structures for Orthogonal Range Queries , 1985, SIAM J. Comput..

[26]  David Wai-Lok Cheung,et al.  A Fast Algorithm for Density-Based Clustering in Large Database , 1999, PAKDD.