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# R* Trees - PowerPoint PPT Presentation

R* Trees. Presenters:- Twisha Surender. R* Trees. Variant of R-tree Supports point and spatial data efficiently at the same time Implementation cost only slightly higher than that of other R-trees. Supports map-overlay operation – Spatial Join

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Presentation Transcript

### R* Trees

Presenters:-

Twisha

Surender

• Variant of R-tree

• Supports point and spatial data efficiently at the same time

• Implementation cost only slightly higher than that of other R-trees.

• Supports map-overlay operation – Spatial Join

• E.g. of Spatial Join queries: Two spatial relations S1 and S2, find all pairs: x in S1, y in S2 s.t. x rel y = true where rel = intersect, inside etc.

• Completely Dynamic

• Optimization Criteria:

• (O1) Area covered by an index MBR

• (O2) Overlap between index MBRs

• (O3) Margin of an index rectangle

• (O4) Storage utilization

• Sometimes it is impossible to optimize all the above criteria at the same time!

• Optimization in ChooseSubTree module for leaf nodes

• Revised Node-Split Algorithm

• Forced Reinsertion at Node Overflow

• ChooseSubtree:

• If next node is a leaf node, choose the node using the following criteria:

• Least overlap enlargement

• Least area enlargement

• Smaller area

• Else

• Least area enlargement

• Smaller area

• Perform better especially inQueries with small query rectangles on datafiles with non-uniformly distributed small rectangles or points

• SplitNode

• Choose the axis to split

• Choose the two groups along the chosen axis

• ChooseSplitAxis

• Along each axis, sort rectangles and break them into two groups (M-2m+2 possible ways where one group contains at least m rectangles). Compute the sum S of all margin-values (perimeters) of each pair of groups. Choose the one that minimizes S

• ChooseSplitIndex

• Along the chosen axis, choose the grouping that gives the minimum overlap-value, then area-value

• Forced Reinsert:

• defer splits, by forced-reinsert, i.e.: instead of splitting, temporarily delete some entries, shrink overflowing MBR, and re-insert those entries

• Which ones to re-insert?

• How many? A: 30%

• OverflowTreatment( parameter level)

• If level is not root level and this is first call to OverflowTreatment for this level

• Then, invoke Reinsert

• Else, invoke Split

• Reinsert

• Sort entries on their distance from center

• Remove first p entries, adjust BR

• Invoke insert to reinsert the entries

• Forced reinsert changes entries between neighboring nodes and decreases the overlap

• Storage utilization is improved

• Due to restructuring, less splits occur

• Since outer rectangles are re-inserted, more quadratic directory rectangles.

• For every query file and every data file less disk accessed are required than any other variants.

• Highly robust against ugly data distributions

• Likely significant improvement over other R tree variants. In spite of forced reinsertion, average insertion cost is not increased but essentially decreased regarding the R-tree variants.

• Efficiently supports point and spatial data at the same time

• Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, Bernhard Seeger: The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles