Session15

Session15 - CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585...

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Unformatted text preview: CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585 Spatial Index Structures (R-tree Family) Instructor: Cyrus Shahabi CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585 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 CSCI585 CSCI585 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 CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585 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 CSCI585 CSCI585 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 CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585 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 CSCI585 CSCI585 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 CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585 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 CSCI585 CSCI585 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 ... CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585 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 ......
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Session15 - CSCI585 CSCI585 C. Shahabi CSCI585 CSCI585...

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