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Session15

# Session15 - CSCI585 Spatial Index Structures(R-tree Family...

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CSCI585 CSCI585 C. Shahabi Spatial Index Structures (R-tree Family) Instructor: Cyrus Shahabi

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CSCI585 CSCI585 C. Shahabi Problem Given a collection of geometric objects (points, lines, polygons, ...) organize them on disk, to answer spatial queries (range, nn, etc)
CSCI585 CSCI585 C. Shahabi Problem Spatial objects – Points, lines, rectangles, regions, … Hierarchical data structures – Based on recursive decomposition, similar to divide and conquer method, like B-tree. Why not B-Tree? – More than one dimension – Concept of closeness relies on all the dimensions of the spatial data

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CSCI585 CSCI585 C. Shahabi R-trees [Guttman 84] Main idea: extend B+-tree to multi-dimensional spaces! – (only deal with Minimum Bounding Rectangles - MBR s)
CSCI585 CSCI585 C. Shahabi Height-balanced tree similar to B-tree for k -dimensions Every leaf node contains between m (m M/2) and M index records, unless it is the root For each index record (I, tuple-identifier) in a leaf node, I is the MBR that contains the n-dimensional data object represented by the indicated tuple Every non-leaf node has between m and M children unless it is the root For each entry (I, child-pointer) in a non-leaf node, I is the MBR that spatially contains the rectangles in the child node. All leaves appear on the same level The root node has at least two children unless it is a leaf

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CSCI585 CSCI585 C. Shahabi Example m=2,M=4: group nearby rectangles to parent MBRs; each group -> disk page A B C D E F G H J I
CSCI585 CSCI585 C. Shahabi Example m=2, M=4 A B C D E F G H I J P1 P2 P3 P4 F G D E H I J A B C

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CSCI585 CSCI585 C. Shahabi Example m=2, M=4 A B C D E F G H I J P1 P2 P3 P4 P1 P2 P3 P4 F G D E H I J A B C
CSCI585 CSCI585 C. Shahabi R-trees - format of nodes {(MBR; obj_ptr)} for leaf nodes P1 P2 P3 P4 A B C x-low; x-high y-low; y-high ... obj ptr ...

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CSCI585 CSCI585 C. Shahabi R-trees - format of nodes {(MBR; node_ptr)} for non-leaf nodes P1 P2 P3 P4 A B C x-low; x-high y-low; y-high ... node ptr ...
CSCI585 CSCI585 C. Shahabi E 2 0 4 6 8 10 2 4 6 8 10 x axis y axis b E f omitted 1 E 2 e d c a h g E 3 E 5 E 6 E 4 E 7 8 contents E 9 i a b c d e f h g E 1 E 2 E 3 E 4 E 5 E 6 E 7 E 8 Root E 9 i E 1 E 2 E 4 E 5 E 8

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CSCI585 CSCI585 C. Shahabi Insertion Processes d e f i g m A B h k l j C X A new index entry X ChooseLeaf Has room Install X Yes SplitNode No C AdjustTree C
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Session15 - CSCI585 Spatial Index Structures(R-tree Family...

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