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

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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

R-trees A Programmer’s 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 Internal nodes 3 2 Tightness Leaf nodes 1 Internal nodes 2 3 Leaf depth equality Kent Williams-King R-trees
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
Algorithms 1 Search 2 Insert AdjustTree 1 3 Delete CondenseTree 1 4 SplitNode Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 R3 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 R4 R3 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 R5 R4 R3 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 R5 R6 R4 R3 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 R5 R6 R7 R4 R3 Kent Williams-King R-trees
R-tree example ( m = 1, M = 3) R1 R2 R5 R6 R8 R7 R4 R3 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) ‘ Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R3 R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R3 R4 R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R3 R4 R5 R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R3 R4 R6 R5 R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R3 R4 R6 R7 R5 R1 Kent Williams-King R-trees
R-tree example ( m = 2, M = 4) R2 R8 R3 R4 R6 R7 R5 R1 Kent Williams-King R-trees

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