1. File Processing : Multi-dimensional Index 2015, Spring Pusan National University Ki-Joune Li

2. STEMPNU Multi-Dimensional Index Multi-Attributes Query vs. Single Attribute Query  Single Attribute : Only ONE attribute to specify query condition Example : Find Students whose record is in [3.5, 4.5]  Multi-Attributes : Several attributes Example : Find students whose height is greater than 180 cm and weight is less than 70 Kg Each attribute corresponds to a dimension  Multi-Attribute Query : Multi-Dimensional Query

3. STEMPNU Processing Multi-dimensional Queries Example : Find students whose height > 180 cm and weight < 70 Kg Method 1 : Using a B+-tree  Step 1 : Apply B+-tree to search student taller than 180 cm  Step 2 : Search students lighter than 70 Kg from the result of step 1  Height and Weight or Weight and Height ? 180 < 70 Result

4. STEMPNU Processing Multi-dimensional Queries Method 2 : Using Two B+-trees  Step 1 : Result 1 ← Students taller than 180 cm by B+-tree  Step 2 : Result 2 ← Students lighter than 70 Kg by B+-tree  Step 3 : Result ← Result 1  Result 2 Comparison of Method 1 and Method 2 180  < 70 Result ==

5. STEMPNU Processing Multi-dimensional Queries Method 3 : Unified Index for Several Attributes  One index for several attributes  Multi-Dimensional Space  Two approaches Extending B+-tree Extending Dynamic Hashing Index for Height and Weight Weight Height

6. STEMPNU block pointer... Block Pointer Array Extending Hashing : Grid Approach Weight Height Query Fixed Variable Fixed Grid Method Grid File

7. STEMPNU Extending Hashing : Grid File Directory (x 1, y 1 )(x 2, y 2 )Block Pointer Query

8. STEMPNU Problem 1: Dead Space Query No objects in this query area 5 block accesses Dead Space  Empty space with no objects How to reduce dead space

9. STEMPNU Minimum Bounding Rectangle Query MBR (Minimum Bounding Rectangle) Only 1 Disk Access

10. STEMPNU Problem 2: Non-Point Object Where to store this object

11. STEMPNU Minimum Bounding Rectangle MBR (Minimum Bounding Box)  Two dimensional geometric simplification of objects  Not the Whole space,  only in the region occupied by objects (X 1min, X 2min ) (X 1max, X 2max )

12. STEMPNU Extending B+-tree : R-tree B+-tree vs. R-tree  B+-tree : Interval (1-D rectangle)  R-tree : Multi-Dimensional Interval (Rectangle) R-tree : Rectangle B+-tree  Each Node MBR (Minimum Bounding Rectangle) instead of Interval (or Delimiter)  No Linked-List for External Nodes  A certain amount of overlapping is indispensable

13. STEMPNU Extending B+-tree : R-tree Example Query Root

14. STEMPNU Upward Split like B-tree Split MBR in the case of overflow  Line sweeping : Compare Cost-X and Cost-Y  Splitting Line New MBR

15. STEMPNU Splitting Strategy 50:50 Split Instead of 50:50 split, other cost measures  Area,  Perimeter  Overlapping Area Good SplitBad Split 1. Make them as COMPACT as possible 2. Preserve spatial proximity as possible

16. STEMPNU R*-tree: An Improvement of R-tree Re-Insertion Strategy on Overflow Most Popular Index for Multi-Dimensional Index Newly Inserted Object Delete and Re-Insert this Overflow Re-Inserted Object More Compact