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The DR-tree: A Main Memory Data Structure for Complex Multi-dimensional Objects

The DR-tree: A Main Memory Data Structure for Complex Multi-dimensional Objects. YOUNG-JU LEE , CHIN-WAN CHUNG. Seung-Hyun Ji Graphics Application Lab. Contents. Introduce Index Structure. Problem of Index Structure. Related Work(TR*-Tree). Introduce DMBR and DR-Tree.

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The DR-tree: A Main Memory Data Structure for Complex Multi-dimensional Objects

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

  2. 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).

  3. Main Memory Data Structure Original Data Secondary Storage Main Memory Data Structure

  4. Index Structure • Index structure for complex object. • MBR • Smallest aligned n-dimensional rectangle enclosing and object. • LSD-Tree, R*-Tree, X-Tree • Region decomposition • Divided into sub-region until a region obtains a desired simple component. • PM quadtree, TR*-Tree

  5. Index structure Problem • MBR • `False hit’ • False hit candidate. • Refinement step • refinement step is very costly. • Region decomposition • Simple component • Quadrants, trapezoid, line segment. • Number of decomposed components could result in a storage and query processing overhead.

  6. Related Work(1/2) • TR*-Tree • Improve R*-Tree • Represent exact geometry spatial attributes • Reduce memory operations • Store components of 1 decomposed object • Internal node • Pointer child node • Minimum bounding rectangle of trapezoids in child • Leaf node • Trapezoids

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

  8. Related Work(3/3) • TR* Tree

  9. DR-Tree(1/3) • DMBR • Decomposition Method For multi-dimension complex object. • Extend to MBR. • Additional Constraint. • Accuracy of the Decomposition(AOD). • split permit above a threshold.

  10. DR-Tree(2/3) • Example of DMBR • AOD(2) : 1/4 • 2D Object • 3D Object

  11. DR-Tree(3/3) • Construction DR-Tree a c b e d

  12. Two-Step Index Structure • Original Object • R*-Tree • Decomposition • DR-Tree

  13. Query Processing • Query Processing • Point Query • Filter Step : R* Tree search algorithm. • Refinement Step : use DR Tree . • Region Query • Filter Step : R* Tree search algorithm. • Traditional decomposition methods not support efficient performance.(number of component) • Small number of components.(DMBR) • Spatial Join Query

  14. State of the art • Genesys index structure • Original Data • Use R*-Tree • Decomposition Method • Use TR* Tree

  15. Performance Analysis(1/3) • Performance • Using real geometric data(park,map,lake,state). • Compare to Genesys(TR* Tree). Query processing time for various spatial queries. IO-time and CPU time

  16. Performance Analysis(2/3) • Performance Storage requirements (saving 71%) Preprocessing cost

  17. Performance Analysis(3/3) • Performance Query processing time and storage requirement for TIGER/Line files.

  18. 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.

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