rbush

High-performance 2D spatial index for rectangles (based on R*-tree with bulk loading and bulk insertion algorithms)

npm install rbush
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RBush

RBush is a high-performance JavaScript library for 2D spatial indexing of points and rectangles by Vladimir Agafonkin, based on an optimized R-tree data structure with bulk insertion support.

Spatial index is a special data structure for points and rectangles that allows you to perform queries like "all items within this bounding box" very efficiently (e.g. hundreds of times faster than looping over all items). It's most commonly used in maps and data visualizations.

Build Status

Demos

The demos contain visualization of trees generated from 50k bulk-loaded random points. Open web console to see benchmarks; click on buttons to insert or remove items; click to perform search under the cursor.

Performance

The following sample performance test was done by generating random uniformly distributed rectangles of ~0.01% area and setting maxEntries to 16 (see debug/perf.js script). Performed with Node.js v0.10.22 on a Retina Macbook Pro 15 (mid-2012).

Test RBush old RTree Improvement
insert 1M items one by one 8.87s 14.6s 1.6x
1000 searches of 0.01% area 0.09s 2.54s 28x
1000 searches of 1% area 0.71s 5.08s 7x
1000 searches of 10% area 3.04s 17.1s 5.6x
remove 1000 items one by one 0.03s 3.32s 110x
bulk insert 1M items 3.53s n/a 4x

Usage

Creating a Tree

var tree = rbush(9);

An optional argument to rbush defines the maximum number of entries in a tree node. It drastically affects the performance, so you should adjust it considering the type of data and search queries you perform.

Adding and Removing Data

Insert an item:

var item = [20, 40, 30, 50]; // [x1, y1, x2, y2]
tree.insert(item);

Remove a previously inserted item:

tree.remove(item);

Clear all items:

tree.clear();

Items inserted in the tree can have other arbitrary properties/elements that you can access later:

var item1 = [20, 40, 30, 50, {foo: 'bar'}];
tree.insert(item1);

var item2 = [15, 15, 30, 30];
item2.foo = 'bar';
tree.insert(item2);

Data Format

By default, RBush assumes the format of data points to be [minX, minY, maxX, maxY]. You can customize this by providing an array with minX, minY, maxX, maxY accessor strings as a second argument to rbush like this:

var tree = rbush(9, ['.minLng', '.minLat', '.maxLng', '.maxLat']);
tree.insert({id: 'foo', minLng: 30, minLat: 50, maxLng: 40, maxLat: 60});

Bulk-Inserting Data

Bulk-insert the given data into the tree:

tree.load([
    [10, 10, 15, 20],
    [12, 15, 40, 64.5],
    ...
]);

Bulk insertion is usually ~2-3 times faster than inserting items one by one. After bulk loading (bulk insertion into an empty tree), subsequent query performance is also ~20-30% better.

When you do bulk insertion into an existing tree, it bulk-loads the given data into a separate tree and inserts the smaller tree into the larger tree. This means that bulk insertion works very well for clustered data (where items are close to each other), but makes query performance worse if the data is scattered.

var result = tree.search([40, 20, 80, 70]);

Returns an array of data items (points or rectangles) that the given bounding box ([minX, minY, maxX, maxY]) intersects.

var allItems = tree.all();

Returns all items of the tree.

Export and Import

// export data as JSON object
var treeData = tree.toJSON();

// import previously exported data
var tree = rbush(9).fromJSON(treeData);

Importing and exporting as JSON allows you to use RBush on both the server (using Node.js) and the browser combined, e.g. first indexing the data on the server and and then importing the resulting tree data on the client for searching.

Algorithms Used

  • single insertion: non-recursive R-tree insertion with overlap minimizing split routine from R-tree (split is very effective in JS, while other R-tree modifications like reinsertion on overflow and overlap minimizing subtree search are too slow and not worth it)
  • single deletion: non-recursive R-tree deletion using depth-first tree traversal with free-at-empty strategy (entries in underflowed nodes are not reinserted, instead underflowed nodes are kept in the tree and deleted only when empty, which is a good compromise of query vs removal performance)
  • bulk loading: OMT algorithm (Overlap Minimizing Top-down Bulk Loading)
  • bulk insertion: STLT algorithm (Small-Tree-Large-Tree)
  • search: standard non-recursive R-tree search

Papers

Development

npm install  # install dependencies

npm test     # check the code with JSHint and run tests
npm run perf # run performance benchmarks
npm run cov  # report test coverage (with more detailed report in coverage/lcov-report/index.html)

Changelog

1.3.2 — Nov 25, 2013

  • Improved removal performance by ~50%. #18

1.3.1 — Nov 24, 2013

  • Fixed minor error in the choose split axis algorithm. #17
  • Much better test coverage (near 100%). #6

1.3.0 — Nov 21, 2013

  • Significantly improved search performance (especially on large-bbox queries — up to 3x faster). #11
  • Added all method for getting all of the tree items. #11
  • Made toBBox, compareMinX, compareMinY methods public, made it possible to avoid Content Security Policy issues by overriding them for custom format. #14 #12

1.2.5 — Nov 5, 2013

  • Fixed a bug where insertion failed on a tree that had all items removed previously. #10

1.2.4 — Oct 25, 2013

  • Added Web Workers support. #9

1.2.3 — Aug 30, 2013

  • Added AMD support. #8

1.2.2 — Aug 27, 2013

  • Eliminated recursion when recalculating node bboxes (on insert, remove, load).

1.2.0 — Jul 19, 2013

First fully functional RBush release.

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