Session18

Session18 - CSCI585 CSCI585 C. Shahabi The Dynamic Data...

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Unformatted text preview: CSCI585 CSCI585 C. Shahabi The Dynamic Data Cube S. Geffner D. Agrawal A. EL Abbadi CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Method Dynamic Data Cube Improving Update Growth of the Cube Conclusion CSCI585 CSCI585 C. Shahabi Measure Attribute Introduction(example) Customer_age Date Dimensional Attribute $390 $590 $560 $950 $800 $500 $370 1 0 / 3 0 $190 $360 $250 $500 $440 $390 $170 1 0 / 2 9 $170 $230 $250 $600 $600 $230 $250 1 0 / 2 8 $250 $500 $470 $800 $790 $550 $800 1 0 / 2 7 $300 $500 $500 $600 $200 $170 $110 1 0 / 2 6 $300 $100 $300 $240 $100 $130 $120 1 0 / 2 5 $150 $600 $250 $500 $700 $400 $300 1 0 / 2 4 2 3 2 2 2 1 2 0 1 9 1 8 1 7 I n d e x CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Methods Dynamic Data Cube Improving Update Growth of the Cube Conclusion 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 6 5 4 3 2 1 I n d e x Size= N 2 CSCI585 CSCI585 C. Shahabi Problem Description (original array A) Observation from array A s Arbitrary range queries : O(n d ) s Update: O(1) d: # of dimension n: size in each dimension CSCI585 CSCI585 C. Shahabi Outline Introduction Problem description Previous Method Dynamic Data Cube Improving Update Growth of the Cube Conclusion 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 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 6 5 4 3 2 1 I n d e x 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 6 5 4 3 2 1 I n d e x Precompute array P Original array A Previous method (prefix sum) 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 6 5 4 3 2 1 I n d e x 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 6 5 4 3 2 1 I n d e x Prefix sum array P Size= N 2 CSCI585 CSCI585 C. Shahabi Observation from array P s Arbitrary range queries : O(1) s Update in worst case: O(n d ) d: # of dimension n: size in each dimension Previous method (prefix sum array P) CSCI585 CSCI585 C. Shahabi Same as for Prefix-sum, DDC can also be applied to obtain count (special case...
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Session18 - CSCI585 CSCI585 C. Shahabi The Dynamic Data...

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