1. Grid Files Multi-dimensional Index Structures

2. Jaruloj Chongstitvatana 2006Grid Files 2 Properties of Grid Files  Support multi-dimensional data, but not high-dimension.  Every key is treated as primary key.  The index structure adapts itself dynamically to maintain storage efficiency.  Guarantee two disk accesses for point queries  Values of key must be in lineraly- ordered domain.

3. Jaruloj Chongstitvatana 2006Grid Files 3 Structure of Index Structure  Grid directories: for k-dimensional data Grid array  A k-dimensional array  Each element is a pointer to a data page Linear scales  k 1-dimensional array  Each array defines the partition of values in each dimension.  Data buckets/ pages

4. Jaruloj Chongstitvatana 2006Grid Files 4 Grid Directory Grid array Pointers to data buckets/pagesLinear scales

5. Jaruloj Chongstitvatana 2006Grid Files 5 Point Query X Y 0 6 25 32 A F K O Z Find x=9 and y=“Rat”

6. Jaruloj Chongstitvatana 2006Grid Files 6 Range Query X Y 0 6 25 32 A F K O Z Find 5<x<9 and “Mat”<y<“Rat”

7. Jaruloj Chongstitvatana 2006Grid Files 7 Insertion Overflow, then split the region Update the linear scaleAlso, split the data page

8. Jaruloj Chongstitvatana 2006Grid Files 8 Insertion Overflow, then split the regionOnly the overflowed data page is split Update linear scale This data page is not split.

9. Jaruloj Chongstitvatana 2006Grid Files 9 Insertion The data page is overflowed, but the directory is notTherefore, split only the data page

10. Jaruloj Chongstitvatana 2006Grid Files 10 Insertion

11. Jaruloj Chongstitvatana 2006Grid Files 11 Merging A CD B FE ECDF AB 1 3 2 1 2 3

12. Jaruloj Chongstitvatana 2006Grid Files 12 Deletion A CD B FE EC D F AB Merge data pages A and B, but directory pages cannot be merged yet. Merge does not occur Delete point

13. Jaruloj Chongstitvatana 2006Grid Files 13 Deletion A CD B FE EC D F AB Merge data pages D and F. Directory pages are also merged. Delete point

14. Jaruloj Chongstitvatana 2006Grid Files 14 Deletion AB DFCE DF AB Merge data pages CE and DF. Directory pages are also merged. Delete point