r trees
play

R-trees A Programmers Introduction Kent Williams-King - PowerPoint PPT Presentation

R-trees A Programmers Introduction Kent Williams-King kawillia@ucalgary.ca March 1, 2011 Introduction 1 What is an R-tree? 2 What are R-trees useful for? Kent Williams-King R-trees Properties 1 Balancing Root node 1 Leaf nodes 2


  1. R-trees A Programmer’s Introduction Kent Williams-King kawillia@ucalgary.ca March 1, 2011

  2. Introduction 1 What is an R-tree? 2 What are R-trees useful for? Kent Williams-King R-trees

  3. Properties 1 Balancing Root node 1 Leaf nodes 2 Internal nodes 3 2 Tightness Leaf nodes 1 Internal nodes 2 3 Leaf depth equality Kent Williams-King R-trees

  4. Tree depth The branching factor of each level of an R-tree is at least m , and at most M , so: ⌈ log m N ⌉ − 1 ≤ depth ≤ ⌈ log M N ⌉ − 1 So: N m M Bound (inclusive) 4 1 2 1-3 4 2 4 0-1 32 4 8 1-2 25,000 15 50 2-3 25,000 2 15 3-4 100,000 2 4 8-16 1 Tree depth is low: why are lookups remotely expensive? Kent Williams-King R-trees

  5. Algorithms 1 Search 2 Insert AdjustTree 1 3 Delete CondenseTree 1 4 SplitNode Kent Williams-King R-trees

  6. R-tree example ( m = 1, M = 3) Kent Williams-King R-trees

  7. R-tree example ( m = 1, M = 3) R1 Kent Williams-King R-trees

  8. R-tree example ( m = 1, M = 3) R1 R2 Kent Williams-King R-trees

  9. R-tree example ( m = 1, M = 3) R1 R2 R3 Kent Williams-King R-trees

  10. R-tree example ( m = 1, M = 3) R1 R2 R4 R3 Kent Williams-King R-trees

  11. R-tree example ( m = 1, M = 3) R1 R2 R5 R4 R3 Kent Williams-King R-trees

  12. R-tree example ( m = 1, M = 3) R1 R2 R5 R6 R4 R3 Kent Williams-King R-trees

  13. R-tree example ( m = 1, M = 3) R1 R2 R5 R6 R7 R4 R3 Kent Williams-King R-trees

  14. R-tree example ( m = 1, M = 3) R1 R2 R5 R6 R8 R7 R4 R3 Kent Williams-King R-trees

  15. R-tree example ( m = 2, M = 4) ‘ Kent Williams-King R-trees

  16. R-tree example ( m = 2, M = 4) R1 Kent Williams-King R-trees

  17. R-tree example ( m = 2, M = 4) R2 R1 Kent Williams-King R-trees

  18. R-tree example ( m = 2, M = 4) R2 R3 R1 Kent Williams-King R-trees

  19. R-tree example ( m = 2, M = 4) R2 R3 R4 R1 Kent Williams-King R-trees

  20. R-tree example ( m = 2, M = 4) R2 R3 R4 R5 R1 Kent Williams-King R-trees

  21. R-tree example ( m = 2, M = 4) R2 R3 R4 R6 R5 R1 Kent Williams-King R-trees

  22. R-tree example ( m = 2, M = 4) R2 R3 R4 R6 R7 R5 R1 Kent Williams-King R-trees

  23. R-tree example ( m = 2, M = 4) R2 R8 R3 R4 R6 R7 R5 R1 Kent Williams-King R-trees

Recommend


More recommend