OLAP (Online Analytical Processing): Iterative Data Cubes Excerpt - PowerPoint PPT Presentation

OLAP (Online Analytical Processing): Iterative Data Cubes Excerpt from Presentation by M. Riedewald 1 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Content � Introduction to Multidimensional Databases (from A.R. 20 and 21) � Focus Application: OLAP � Prefix-Sum Data Cube (from A.R. 16) � Dynamic Data Cube (from A.R. 17) � Iterative Data Cube (from A.R. 18) � Wavelet-based approaches • Compact Data Cube (from A.R. 19) • ProPolyne (from A.R. 22 and 23) 2 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Iterative Data Cube Flexible Data Cubes for Online Aggregation Mirek Riedewald, Divyakant Agrawal, and Arm El Abbadi Space-Efficient Data Cubes for Dynamic Environments Mirek Riedewald, Divyakant Agrawal, Arm El Abbadi, and Renato Pajarola 3 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Outline � What is IDC? � Pre-Aggregation Techniques � Querying and Updating an IDC � Selecting an IDC � IDC with more than One Dimension � Conclusion 4 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Iterative Data Cube (IDC) � Provides a modular framework for combining one- dimensional aggregation techniques to create space- optimal high-dimensional data cubes. � For each dimension a different one-dimensional technique can be selected. � Combining the one-dimensional techniques is easy. � Allows a variety of cost tradeoffs between query and update. � Generalizes some of the pre-aggregation approaches: � PS (Prefix Sum) � SRPS (Space-Efficient Relative Prefix Sum) � SDDC (Space-Efficient Dynamic Data Cube) 5 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Prefix Sum (review) Original array 3 5 1 2 2 4 6 3 3 ………… PS array 3 8 9 11 13 17 23 26 29 6 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum � The data cube is partitioned into a set of disjoint hyper-rectangles of equal size (termed boxes ) � Any cell in box B stores the value: SUM(A[l 1 , l 2 , …, l d ]:A[c]) where for all i: 1 <= i <= d l i =0 , if c i =a i l i =a i +1 , if a i +1 <= c i < a i +k 7 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 0 3 5 1 2 2 4 6 3 3 1 5 1 7 3 2 6 8 7 1 2 4 2 2 2 4 2 3 3 3 4 5 7 3 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 8 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 0 3 5 1 2 2 4 6 3 3 1 5 1 7 3 2 6 8 7 1 2 4 2 9 7 2 2 4 2 3 3 3 4 5 7 3 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 9 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 0 3 5 1 2 2 4 6 3 3 1 5 1 7 3 2 6 8 7 1 2 4 2 9 7 11 2 2 4 2 3 3 3 4 5 7 3 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 10 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 11 0 3 5 1 2 2 4 6 3 3 1 5 18 1 7 3 2 6 8 7 1 2 4 2 9 7 11 2 2 4 2 3 3 3 4 5 7 3 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 11 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 11 0 3 5 1 2 2 4 6 3 3 1 5 18 1 7 3 2 6 8 7 1 2 4 2 9 7 11 2 2 4 2 3 3 3 4 5 7 3 15 14 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 12 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 11 0 3 5 1 2 2 4 6 3 3 1 5 18 1 7 3 2 6 8 7 1 2 4 2 9 7 11 29 2 2 4 2 3 3 3 4 5 7 3 15 14 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 13 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 11 0 3 5 1 2 2 4 6 3 3 1 5 18 1 7 3 2 6 8 7 1 2 4 2 9 7 11 29 2 2 4 2 3 3 3 4 5 7 3 15 14 20 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 14 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 11 0 3 5 1 2 2 4 6 3 3 1 5 18 1 7 3 2 6 8 7 1 2 4 2 9 7 11 29 2 2 4 2 3 3 3 4 5 7 3 15 14 20 51 3 3 2 1 5 3 5 2 8 2 4 4 4 2 1 3 3 4 7 1 3 5 5 2 3 3 6 1 8 5 1 1 6 6 4 5 2 7 1 9 3 3 4 7 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 8 15 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 6 11 6 23 6 0 3 5 1 2 2 4 6 3 3 1 5 18 15 34 6 1 7 3 2 6 8 7 1 2 4 2 9 7 11 29 11 21 55 7 18 2 2 4 2 3 3 3 4 5 7 3 15 14 20 51 16 35 99 18 34 3 3 2 1 5 3 5 2 8 2 4 3 10 7 24 4 4 4 2 1 3 3 4 7 1 3 5 6 5 9 24 4 16 52 2 6 5 2 3 3 6 1 8 5 1 1 6 25 24 36 93 21 61 23 47 182 6 4 5 2 7 1 9 3 3 4 7 6 10 4 23 4 7 2 4 2 2 3 1 9 1 3 8 7 8 13 23 6 9 42 10 19 8 5 4 3 1 3 2 1 9 6 16 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 0 3 5 6 11 2 6 23 3 6 0 3 5 1 2 2 4 6 3 3 1 7 3 5 18 8 15 34 2 6 1 7 3 2 6 8 7 1 2 4 2 9 7 11 29 11 21 55 7 18 2 2 4 2 3 3 3 4 5 7 3 15 14 20 51 16 35 99 18 34 3 3 2 1 5 3 5 2 8 2 4 4 2 3 10 3 7 24 1 4 4 4 2 1 3 3 4 7 1 3 5 6 5 9 24 4 16 52 2 6 5 2 3 3 6 1 8 5 1 1 6 25 24 36 93 21 61 23 47 182 6 4 5 2 7 1 9 3 3 4 7 2 4 6 10 3 4 23 1 4 7 2 4 2 2 3 1 9 1 3 8 7 8 13 23 6 9 42 10 19 8 5 4 3 1 3 2 1 9 6 17 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) SRPS array (block size 3) Original array 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 0 0 0 0 3 3 5 5 1 1 2 2 2 2 4 4 6 6 3 3 3 3 Inner cells Border cells 1 1 1 1 7 7 3 3 2 2 6 6 8 8 7 7 1 1 2 2 4 4 2 2 2 2 2 2 4 4 2 2 3 3 3 3 3 3 4 4 5 5 7 7 3 3 3 3 3 3 2 2 1 1 5 5 3 3 5 5 2 2 8 8 2 2 4 4 4 4 4 4 2 2 1 1 3 3 3 3 4 4 7 7 1 1 3 3 Inner cells store Border cells include cells 5 5 5 5 2 2 3 3 3 3 6 6 1 1 8 8 5 5 1 1 1 1 sums local to the from outside the block 6 6 6 6 4 4 5 5 2 2 7 7 1 1 9 9 3 3 3 3 4 4 block. into their aggregation. 7 7 7 7 2 2 4 4 2 2 2 2 3 3 1 1 9 9 1 1 3 3 8 8 5 5 4 4 3 3 1 1 3 3 2 2 1 1 9 9 6 6 8 8 Partition into blocks of equal size 18 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) Original array 3 5 1 2 2 4 6 3 3 SRPS array (block size 3) 19 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani

Space-Efficient Relative Prefix Sum (cont’d) Original array 3 5 1 2 2 4 6 3 3 SRPS array 6 6 6 (block size 3) 20 4/14/2008 USC - CSCI585 - Spring 2008 - Farnoush Banaei-Kashani