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Unformatted text preview: CSE5120Fall2009 RTrees: Index structure for Spatial Searching Guttman, SIGMOD 1984 Rtree : • a heightbalanced tree • has some similarity to a Btree • records in its leaf nodes pointing to data objects. An Rtree for spatial objects A B C D E F G H J K I N M L A B C D E F G H I J K L M N . . . . . . xl xh yl yh . . . pointer to child An Rtree for data points A B C D E F G H J K I N M L A B C D E F G H I J K L M N point x point x is under A only point y point y is under B only Leaf nodes contain ( I, object identifier ) I is an ndimensional rectangle which is the bounding box of the spatial object I = ( I , I 1 , ..., I n 1 ) I i is an interval [a,b] Nonleaf nodes contain ( I, child pointer ) where I covers all rectangles in the lower node’s entries. Node size: maximum M , minimum m ≤ l M 2 m 47 Some properties of an Rtree: 1. In a leaf node, I is the smallest rectangle that contains the ndimensional data ob ject. 2. For each entry in a nonleaf node, I is the smallest rectangle that contains the rectan gles in the child node. 3. The root node has at least two children un less it is a leaf, and at most M children. 4. All leaves appear on the same level. The height of an Rtree containing N index records is at most  log m N   1 The maximum number of nodes is » N m … + » N m 2 … + ... + 1 Worst case space utilization for all nodes ex cept the root is m M . Range Search A B C D E F G H J K I N M L A B C D E F G H I J K L M N Query Range Search Similar to Btree in some way. However, more than one subtree under a node may be visited, not possible to guarantee good perfor mance . Algorithm Search : Given: an Rtree, Query: a search rectangle Q. 1. search subtrees check each entry E to see if E.I overlaps Q ....
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 Fall '09
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