lec40 - R-Trees Extension of B-trees Collection of...

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R-Trees Extension of B+-trees. Collection of d-dimensional rectangles. A point in d-dimensions is a trivial rectangle.
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Non-rectangular Data Non-rectangular data may be represented by minimum bounding rectangles (MBRs).
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Operations Insert Delete Find all rectangles that intersect a query rectangle. Good for large rectangle collections stored on disk.
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R-Trees—Structure Data nodes (leaves) contain rectangles. Index nodes (non-leaves) contain MBRs for data in subtrees. MBR for rectangles or MBRs in a non-root node is stored in parent node.
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R-Trees—Structure R-tree of order M. Each node other than the root has between m <= ceil(M/2) and M rectangles/MBRs. Assume m = ceil(M/2) henceforth. Typically, m = ceil(M/2). Root has between 1 and M rectangles/MBRs. Each index node has as many MBRs as children. All data nodes are at the same level.
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Example R-tree of order 4. Each node may have up to 4 rectangles/MBRs.
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Example Possible partitioning of our example data into 12 leaves.
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Example Possible R-tree of order 4 with 12 leaves. a b c d e f g h i j k l m n o p Leaves are data nodes that contain 4 input rectangles each. a-p are MBRs
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Example Possible corresponding grouping. a b c d m a b cd e f g h i j k l m n o p
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Example a b c d m e f n Possible corresponding grouping. a b cd e f g h i j k l m n o p
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Example a b c d m e f n h g i o p Possible corresponding grouping. a b cd e f g h i j k l m n o p
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Query Report all rectangles that intersect a given rectangle.
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Query Start at root and find all MBRs that overlap query.
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