mirror of https://github.com/tidwall/tile38.git
89 lines
3.2 KiB
Markdown
89 lines
3.2 KiB
Markdown
# `R!tree`
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[](https://godoc.org/github.com/tidwall/rbang)
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This package provides an in-memory R-Tree implementation for Go. It's designed
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for [Tile38](https://github.com/tidwall/tile38) and is optimized for fast rect
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inserts and replacements.
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<img src="cities.png" width="512" height="256" border="0" alt="Cities">
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## Usage
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### Installing
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To start using R!Tree, install Go and run `go get`:
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```sh
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$ go get -u github.com/tidwall/rbang
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```
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### Basic operations
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```go
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// create a 2D RTree
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var tr rbang.RTree
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// insert a point
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tr.Insert([2]float64{-112.0078, 33.4373}, [2]float64{-112.0078, 33.4373}, "PHX")
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// insert a box
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tr.Insert([2]float64{10, 10}, [2]float64{20, 20}, "rect")
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// search
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tr.Search([2]float64{-112.1, 33.4}, [2]float64{-112.0, 33.5},
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func(min, max [2]float64, value interface{}) bool {
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println(value.(string)) // prints "PHX"
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},
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)
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// delete
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tr.Delete([2]float64{-112.0078, 33.4373}, [2]float64{-112.0078, 33.4373}, "PHX")
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```
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## Algorithms
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This implementation is a variant of the original paper:
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[R-TREES. A DYNAMIC INDEX STRUCTURE FOR SPATIAL SEARCHING](http://www-db.deis.unibo.it/courses/SI-LS/papers/Gut84.pdf)
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### Inserting
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Same as the original algorithm. From the root to the leaf, the boxes which will incur the least enlargment are chosen. Ties go to boxes with the smallest area.
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### Deleting
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Same as the original algorithm. A target box is deleted directly. When the number of children in a box falls below it's minumum entries, it is removed from the tree and it's items are re-inserted.
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### Splitting
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This is a custom algorithm.
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It attempts to minimize intensive operations such as pre-sorting the children and comparing overlaps & area sizes.
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The desire is to do simple single axis distance calculations each child only once, with a target 50/50 chance that the child might be moved in-memory.
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When a box has reached it's max number of entries it's largest axis is calculated and the box is split into two smaller boxes, named `left` and `right`.
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Each child boxes is then evaluated to determine which smaller box it should be placed into.
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Two values, `min-dist` and `max-dist`, are calcuated for each child.
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- `min-dist` is the distance from the parent's minumum value of it's largest axis to the child's minumum value of the parent largest axis.
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- `max-dist` is the distance from the parent's maximum value of it's largest axis to the child's maximum value of the parent largest axis.
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When the `min-dist` is less than `max-dist` then the child is placed into the `left` box.
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When the `max-dist` is less than `min-dist` then the child is placed into the `right` box.
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When the `min-dist` is equal to `max-dist` then the child is placed into an `equal` bucket until all of the children are evaluated.
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Each `equal` box is then one-by-one placed in either `left` or `right`, whichever has less children.
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## Performance
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In my testing:
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- Insert show similar performance as the quadratic R-tree and ~1.2x - 1.5x faster than R*tree.
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- Search and Delete is ~1.5x - 2x faster than quadratic and about the same as R*tree.
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I hope to provide more details in the future.
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## License
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`rbang` source code is available under the MIT License.
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