1. Graphics Application Lab The DR-tree: A Main Memory Data Structure for Complex Multi-dimensional Objects Seung-Hyun Ji Graphics Application Lab YOUNG-JU LEE, CHIN-WAN CHUNG

2. Graphics Application Lab Contents  Introduce Index Structure.  Problem of Index Structure.  Related Work(TR*-Tree).  Introduce DMBR and DR-Tree.  Compare to state-of-the-art index structure(GENESYS). 2

3. Graphics Application Lab Main Memory Data Structure 3 Original Data Secondary Storage Main Memory Data Structure

4. Graphics Application Lab Index Structure  Index structure for complex object. oMBR Smallest aligned n-dimensional rectangle enclosing and object.  LSD-Tree, R*-Tree, X-Tree oRegion decomposition Divided into sub-region until a region obtains a desired simple component.  PM quadtree, TR*-Tree 4

5. Graphics Application Lab Index structure Problem  MBR o`False hit’ False hit candidate. oRefinement step refinement step is very costly.  Region decomposition oSimple component Quadrants, trapezoid, line segment. oNumber of decomposed components could result in a storage and query processing overhead. 5

6. Graphics Application Lab Related Work(1/2)  TR*-Tree oImprove R*-Tree Represent exact geometry spatial attributes Reduce memory operations Store components of 1 decomposed object oInternal node Pointer child node Minimum bounding rectangle of trapezoids in child oLeaf node Trapezoids 6

7. Graphics Application Lab 7 R1 R2 A A B B C C D D E EF 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 9 9 10 11 12 13 14 15 F 8 Related Work(2/3)  TR* Tree

8. Graphics Application Lab Related Work(3/3)  TR* Tree 8

9. Graphics Application Lab DR-Tree(1/3)  DMBR oDecomposition Method For multi-dimension complex object. oExtend to MBR. oAdditional Constraint. Accuracy of the Decomposition(AOD). split permit above a threshold. 9

10. Graphics Application Lab DR-Tree(2/3)  Example of DMBR oAOD(2) : 1/4 2D Object 3D Object 10

11. Graphics Application Lab DR-Tree(3/3)  Construction DR-Tree 11 a b c d e

12. Graphics Application Lab Two-Step Index Structure  Original Object oR*-Tree  Decomposition oDR-Tree 12

13. Graphics Application Lab Query Processing  Query Processing oPoint Query Filter Step : R* Tree search algorithm. Refinement Step : use DR Tree. oRegion Query Filter Step : R* Tree search algorithm. Traditional decomposition methods not support efficient performance.(number of component) Small number of components.(DMBR) oSpatial Join Query 13

14. Graphics Application Lab State of the art  Genesys index structure oOriginal Data Use R*-Tree oDecomposition Method Use TR* Tree 14

15. Graphics Application Lab Performance Analysis(1/3)  Performance oUsing real geometric data(park,map,lake,state). oCompare to Genesys(TR* Tree). 15 Query processing time for various spatial queries. IO-time and CPU time

16. Graphics Application Lab Performance Analysis(2/3)  Performance 16 Storage requirements (saving 71%) Preprocessing cost

17. Graphics Application Lab Performance Analysis(3/3)  Performance 17 Query processing time and storage requirement for TIGER/Line files.

18. Graphics Application Lab Conclusion  Proposed a main memory data structure for complex multi-dimensional object.  Extension of an existing index structure  Reduce processing time.  Reduce the amount of storage.  Easier to implement and applicable to various spatial data. 18