Session19

Session19 - Flexible Data Cubes for Online Aggregation...

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Unformatted text preview: Flexible Data Cubes for Online Aggregation Mirek Riedewald, Divyakant Agrawal, and Arm El Abbadi CSCI585 CSCI585 C. Shahabi (Space-Efficient Data Cubes for Dynamic Environments Mirek Riedewald, Divyakant Agrawal, Arm El Abbadi, and Renato Pajarola ) CSCI585 CSCI585 C. Shahabi Outline Introduction New Approach: IDC Pre-Aggregation Techniques Query and Update an IDC Selecting an IDC IDC with more than One Dimension Conclusion CSCI585 CSCI585 C. Shahabi Introduction Data Cubes s Similar to a multidimensional array s Used in OLAP (Online Analytical Processing) Aggregate range query s It selects range of the data cube and computes the aggregate of the values of the cells in the region. CSCI585 CSCI585 C. Shahabi Introduction Pre-aggregate data cube s Provide fast replies for the queries s Increase update costs and storage costs. New approach s Iterative Data Cube (IDC) CSCI585 CSCI585 C. Shahabi Outline Introduction New Approach: IDC New Approach: IDC Pre-Aggregation Techniques Query and Update an IDC Selecting an IDC IDC with more than One Dimension Conclusion CSCI585 CSCI585 C. Shahabi New Approach Iterative Data Cube (IDC) s Provide a modular framework for combining one-dimensional aggregation techniques to create space- optimal high-dimensional data cubes. CSCI585 CSCI585 C. Shahabi Iterative Data Cube (IDC) Contributions s For each dimension a different one- dimensional technique can be selected. s Combining the one-dimensional techniques is easy. s A variety of cost tradeoffs between query and update. s Generalizing some of pre-aggregation approaches. CSCI585 CSCI585 C. Shahabi Iterative Data Cube Technique IDC is constructed by applying one- dimensional pre-aggregation techniques along the dimensions. Iterative Data Cubes generalize PS, SRPS, and SDDC. s PS (Prefix Sum) s SRPS (Space-Efficient Relative Prefix Sum) s SDDC (Space-Efficient Dynamic Data Cube) CSCI585 CSCI585 C. Shahabi Outline Introduction New Approach: IDC Pre Pre-- Aggregation Techniques Aggregation Techniques Query and Update an IDC Selecting an IDC IDC with more than One Dimension Conclusion CSCI585 CSCI585 C. Shahabi Prefix Sum 3 5 1 2 2 4 6 3 3 Original array PS array 29 26 23 17 13 11 9 8 3 CSCI585 CSCI585 C. Shahabi 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 CSCI585 CSCI585 C. Shahabi 1 2 3 4 5 6 7 8 3 5 1 2 2 4 6 3 3 1 7 3 2 6 8 7 1 2 4 2 2 4 2 3 3 3 4 5 7 3 3 2 1 5 3 5 2 8 2 4 4 2 1 3 3 4 7 1 3 5 2 3 3 6 1 8 5 1 1 6 4 5 2 7 1 9 3 3 4 7 2 4 2 2 3 1 9 1 3 8 5 4 3 1 3 2 1 9 6 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Space-Efficient Relative Prefix Sum Original array SRPS array (block size 3) Partition into blocks of equal size 6 9 1 2 3 1 3 4 5 8 3 1 9 1 3 2 2 4 2 7 4 3 3 9 1 7 2 5 4 6 1 1 5 8 1 6 3 3 2 5 3 1 7 4 3 3 1 2...
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Session19 - Flexible Data Cubes for Online Aggregation...

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