RBushen

RBushen is N-dimensional version of RBush. Inspired by the RBush-3D.

Work-in-progress

This project is a work-in-progress. I was inspired by the RBush-3d that implemented one more dimension to the 2D version. I thought it useful to allow for as many dimensions as one might want. I am thinking of adding Parallel.js to this mix too, but first things first. I'm switching XYZ parameters to be free variables and calling them just indexed vectors. I intend the usage paradigm to follow the same lines as before.

This work has not progressed since 2018 mostly because I found a workaround on my 3D environment that enabled me to achieve the performance I wanted. That did still not mean this indexing mechanism was obsolete. Rather that the use case is different.

Usage

Creating a Tree

var tree = rbushen();

An optional argument to rbushen defines the maximum number of entries in a tree node. 16 (used by default) is a reasonable choice for most applications. Higher value means faster insertion and slower search, and vice versa.

var tree = rbushen(16);

Adding Data

Insert an item:

var item = {
  minX: 20,
  minY: 40,
  minZ: 60,
  maxX: 30,
  maxY: 50,
  maxZ: 70,
  foo: "bar"
};
tree.insert(item);

Removing Data

Remove a previously inserted item:

tree.remove(item);

By default, RBush-3D removes objects by reference. However, you can pass a custom equals function to compare by value for removal, which is useful when you only have a copy of the object you need removed (e.g. loaded from server):

tree.remove(itemCopy, function(a, b) {
  return a.id === b.id;
});

Remove all items:

tree.clear();

Data Format

By default, RBush-3D assumes the format of data points to be an object with minX, minY, minZ, maxX, maxY and maxZ properties. You can customize this by providing an array with corresponding accessor strings as a second argument to rbushen like this:

var tree = rbushen(16, ["[0]", "[1]", "[2]", "[0]", "[1]", "[2]"]); // accept [x, y, z] points
tree.insert([20, 50, 80]);

Bulk-Inserting Data

Bulk-insert the given data into the tree:

tree.load([item1, item2, ...]);

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.

Note that 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 in one update are close to each other), but makes query performance worse if the data is scattered.

Search

var result = tree.search({
  minX: 40,
  minY: 20,
  minZ: 50,
  maxX: 80,
  maxY: 70,
  maxZ: 90
});

Returns an array of data items (points or rectangles) that the given bounding box intersects.

Note that the search method accepts a bounding box in {minX, minY, minZ, maxX, maxY, maxZ} format regardless of the format specified in the constructor (which only affects inserted objects).

var allItems = tree.all();

Returns all items of the tree.

Collisions

var result = tree.collides({
  minX: 40,
  minY: 20,
  minZ: 50,
  maxX: 80,
  maxY: 70,
  maxZ: 90
});

Returns true if there are any items intersecting the given bounding box, otherwise false.

Export and Import

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

// import previously exported data
var tree = rbushen(16).fromJSON(treeData);

Importing and exporting as JSON allows you to use RBush-3D 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.

Note that the nodeSize option passed to the constructor must be the same in both trees for export/import to work properly.

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 v8.9.1 on a MacBook Pro (15-inch, 2017).

Test	RBush-3D	RBush (2D version)
insert 1M items one by one	4.30s	2.94s
1000 searches of 0.01% area	0.02s	0.03s
1000 searches of 1% area	0.09s	0.31s
1000 searches of 10% area	0.73s	1.80s
remove 1000 items one by one	0.02s	0.02s
bulk-insert 1M items	1.40s	1.17s

TODO: Need to update benchmarking results.

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) combined with Floyd–Rivest selection algorithm
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)
npm run viz  # show 3d visualization in browser

Kjue/rbushen