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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 (SpaceEfficient Data Cubes for Dynamic Environments Mirek Riedewald, Divyakant Agrawal, Arm El Abbadi, and Renato Pajarola ) CSCI585 CSCI585 C. Shahabi Outline Introduction New Approach: IDC PreAggregation 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 Preaggregate 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 PreAggregation 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 onedimensional aggregation techniques to create space optimal highdimensional 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 onedimensional techniques is easy. s A variety of cost tradeoffs between query and update. s Generalizing some of preaggregation approaches. CSCI585 CSCI585 C. Shahabi Iterative Data Cube Technique IDC is constructed by applying one dimensional preaggregation techniques along the dimensions. Iterative Data Cubes generalize PS, SRPS, and SDDC. s PS (Prefix Sum) s SRPS (SpaceEfficient Relative Prefix Sum) s SDDC (SpaceEfficient 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 SpaceEfficient Relative Prefix Sum The data cube is partitioned into a set of disjoint hyperrectangles 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 SpaceEfficient 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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 Spring '09

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