1. Data Management+ Laboratory Dynamic Skylines Considering Range Queries Speaker: Adam Adviser: Yuling Hsueh 16th International Conference, DASFAA 2011 Wen-Chi Wang En Tzu Wang Arbee L.P. Chen3

2. INTRODUCTION  What is “Skyline” ? DM+  Page 2

3. INTRODUCTION  Dynamic skyline considering query -Dynamic skyline query regarding query q retrieves the data points not dynamically dominated by any other data points, with respect to q.  Dynamically dominated -A data point t (t[1], t[2],…,t[n]) is defined to dynamically dominate another data point s (s[1], s[2],…,s[n]), with respect to query q (q[1], q[2],…,q[n]), iff 1)|t[i] − q[i]| ≤ |s[i] − q[i]|, ∀ i = 1 to n, and 2)at least in one dimension, say j, |t[j] − q[j]| < |s[j] − q[j]|. DM+  Page 3

4. INTRODUCTION 1)|t[i] − q[i]| ≤ |s[i] − q[i]|, ∀ i = 1 to n, and 2)at least in one dimension, say j, |t[j] − q[j]| < |s[j] − q[j]|. DM+  Page 4

5. INTRODUCTION  We turn to find the skyline in a transferred dataset in which all of the data points in the original space are transferred to the other space whose origin is equal to query. DM+  Page 5

6. INTRODUCTION DM+  Page 6

7. INTRODUCTION  Dynamic skyline considering range queries DM+  Page 7

8. PRELIMINARIES  Problem Formulation -Given an n-dimensional dataset D and a range query q ([q1, q1'], [q2, q2'], …, [qn, qn']), where [qi, qi'] is an interval representing the user interests in the ith dimension, ∀ i = 1 to n, the dynamic skyline query regarding q returns the data points from D, not dynamically dominated by any other data points, with respect to q. DM+  Page 8

9. PRELIMINARIES DM+  Page 9

10. PRELIMINARIES DM+  Page 10  query q ([15, 20], [20, 25]), p8 = (17, 30)  (|17 − 17|, |30 − 25|) = (0, 5)  P7  (|25 − 20|, |25 - 25|) = (5, 0), p3  (|25 − 20|, |5 − 20|) = (5, 15)

11. PRELIMINARIES DM+  Page 11  Data Structures Used in Algorithm -Grid index -Multidirectional Z-order curves  Grid index -Each dimension of the n-dimensional space is partitioned into b blocks, each associated with an equal domain range of r.

12. PRELIMINARIES DM+  Page 12

13. PRELIMINARIES DM+  Page 13  Query cells: (3, 4), (3, 5), (4, 4), and (4, 5), range form: ([3, 4], [4, 5])  Pivot cells:([0, 2], [4, 5]), ([5, 7], [4, 5]), ([3, 4], [0, 3]), and ([3, 4], [6, 7])

14. PRELIMINARIES DM+  Page 14  Z-order curve -point (5, 4) = (101, 100) -the Z-address of (5, 4) is (110010)  Monotonic Ordering of Z-order curve -a data point in a cell with a former order cannot be dominated by the data points in the cells with the latter order

15. PRELIMINARIES DM+  Page 15  Query (3, 4), p4 = (4, 4)  (1, 0), p1 = (1, 6 )  (2, 2)

16. PRELIMINARIES DM+  Page 16

17. Dynamic Skyline Processing DM+  Page 17  Principle of Pruning Strategies

18. Dynamic Skyline Processing DM+  Page 18  Principle of Pruning Strategies

19. Dynamic Skyline Processing DM+  Page 19  Principle of Pruning Strategies

20. ALGORITHM DM+  Page 20

21. EXPERIMENT DM+  Page 21

22. EXPERIMENT DM+  Page 22

23. EXPERIMENT DM+  Page 23

24. CONCLUSIONS DM+  Page 24  Author propose a new problem on dynamic skyline computation regarding a range query.  To efficiently answer this query, Author propose an approach based on the gird index and a newly designed variant of the well-known Z-order curve. By these two components, three efficient pruning strategies are devised, thus avoiding the need to scan the whole dataset for generating the transferred dataset and also reducing the times of dominance checking.

25. THE END Thank you for listening! DM+  Page 25

26. THE END Q & A DM+  Page 26