Session18 - CSCI585 The Dynamic Data Cube S Geffner D...

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CSCI585 CSCI585 C. Shahabi The Dynamic Data Cube S. Geffner D. Agrawal A. EL Abbadi
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CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Method Dynamic Data Cube Improving Update Growth of the Cube Conclusion
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CSCI585 CSCI585 C. Shahabi Measure Attribute Introduction(example) Customer_age Date Dimensional Attribute $390 $590 $560 $950 $800 $500 $370 10/30 $190 $360 $250 $500 $440 $390 $170 10/29 $170 $230 $250 $600 $600 $230 $250 10/28 $250 $500 $470 $800 $790 $550 $800 10/27 $300 $500 $500 $600 $200 $170 $110 10/26 $300 $100 $300 $240 $100 $130 $120 10/25 $150 $600 $250 $500 $700 $400 $300 10/24 23 22 21 20 19 18 17 Index
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CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Methods Dynamic Data Cube Improving Update Growth of the Cube Conclusion
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CSCI585 CSCI585 C. Shahabi Problem Description (original array A) 1 9 1 3 2 2 4 2 7 3 2 1 8 5 2 3 7 3 9 1 7 2 5 4 6 5 8 1 6 3 3 2 5 7 4 3 3 1 2 4 4 2 5 3 5 1 2 3 3 4 3 3 3 2 4 2 2 1 7 8 6 2 3 7 1 6 4 2 2 1 5 3 0 6 5 4 3 2 1 0 Index Size= N 2
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CSCI585 CSCI585 C. Shahabi Problem Description (original array A) Observation from array A square6 Arbitrary range queries : O(n d ) square6 Update: O(1) d: # of dimension n: size in each dimension
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CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Method Dynamic Data Cube Improving Update Growth of the Cube Conclusion
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CSCI585 CSCI585 C. Shahabi Previous method (prefix sum) Precompute many prefix sums of the data cube, which can then be used to answer queries at run time
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CSCI585 CSCI585 C. Shahabi 230 205 168 127 103 69 55 27 7 206 172 142 117 88 62 26 7 182 154 115 93 61 49 25 6 151 126 95 75 50 40 21 5 123 103 80 61 15 35 19 4 99 86 67 51 35 29 15 3 78 67 53 40 29 24 12 2 57 50 93 29 21 18 10 1 23 17 13 11 9 8 3 0 6 5 4 3 2 1 0 Index 1 9 1 3 2 2 4 2 7 3 2 1 8 5 2 3 7 3 9 1 7 2 5 4 6 5 8 1 6 3 3 2 5 7 4 3 3 1 2 4 4 2 5 3 5 1 2 3 3 4 3 3 3 2 4 2 2 1 7 8 6 2 3 7 1 6 4 2 2 1 5 3 0 6 5 4 3 2 1 0 Index Precompute array P Original array A Previous method (prefix sum)
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CSCI585 CSCI585 C. Shahabi Query in Prefix sum? Prefix sum array P 230 205 168 127 103 69 55 27 7 206 172 142 117 88 62 26 7 182 154 115 93 61 49 25 6 151 126 95 75 50 40 21 5 123 103 80 61 15 35 19 4 99 86 67 51 35 29 15 3 78 67 53 40 29 24 12 2 57 50 93 29 21 18 10 1 23 17 13 11 9 8 3 0 6 5 4 3 2 1 0 Index
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CSCI585 CSCI585 C. Shahabi Update in Prefix sum? 230 205 168 127 103 69 55 27 7 206 172 142 117 88 62 26 7 182 154 115 93 61 49 25 6 151 126 95 75 50 40 21 5 123 103 80 61 15 35 19 4 99 86 67 51 35 29 15 3 78 67 53 40 29 * 24 12 2 57 50 93 29 21 18 10 1 23 17 13 11 9 8 3 0 6 5 4 3 2 1 0 Index Prefix sum array P Size= N 2
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CSCI585 CSCI585 C. Shahabi Observation from array P square6 Arbitrary range queries : O(1) square6 Update in worst case: O(n d ) d: # of dimension n: size in each dimension Previous method (prefix sum array P)
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CSCI585 CSCI585 C. Shahabi Same as for Prefix-sum, DDC can also be applied to obtain count (special case of SUM) and average (SUM/COUNT). Generalization: applicable to any binary operator + which has an inverse operator – such that a+b-b=a We focus on SUM
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CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Methods Dynamic Data Cube Improving Update Growth of the Cube Conclusion
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CSCI585 CSCI585 C. Shahabi Dynamic data cube Overlay Box?
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