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BK-Tree implementation in Ruby

BK-trees can be used to efficiently locate strings' best matches from within a large set. If you don’t know what a BK-tree is, these links should provide a good explanation and introduction.

Installation

BK is available as a Ruby gem:

gem install bk

Usage

require "bk"
tree = BK::Tree.new # Use the default Levenshtein distance algorithm

Add items to the tree:

tree.add "cat"
tree.add "dog"
tree.add "monkey"
tree.add "donkey"

Find all items within distance 1 of ‘munkey’:

tree.query("munkey", 1)
# => {"monkey"=>1}

Find all items within distance 2 of ‘munkey’:

tree.query("munkey", 2)
# => {"donkey"=>2, "monkey"=>1}

You can specify a custom distance algorithm by passing an object that responds to call(a, b) with a number:

custom_algorithm = lambda{ |a, b|
  Text::Levenshtein.distance(a, b)
}

tree = BK::Tree.new(custom_algorithm)

Note that:

  1. the result of call must satisfy the triangle inequality, i.e. d(x,z) ≤ d(x,y) + d(y,z); and
  2. whilst a lambda can be used as the distancer, for exporting and importing (described below) to work, a named class must be used.

The precomputed tree can be exported to and reimported later from an IO-like object:

File.open("tree", "wb") do |f|
  tree.export(f)
end

File.open("tree", "rb") do |f|
  tree = BK::Tree.import(f)
end

Performance

Results of looking for words within distance 1 of ‘alien’ in a 20,000-word dictionary:

Loading 20000 words from dictionary ... 0.273s
Building tree ... 57.331s
Linear scan to find expected terms ... 5.711s
Query tree ... 0.133s
2.1% of tree was queried

This means that the BK-tree is about 40 times as fast as a linear search, although building the initial tree took 10 times as long as a linear search.

As the threshold increases, the benefit is reduced. At threshold 3:

Query tree ... 3.368s
62.9% of tree was queried

Limitations

  • Memory usage: around 6 MB for a 20,000-word tree.
  • Maximum tree depth is limited by the stack.

Testing

rake test

...or, for specific tests:

ruby -Itest test/test_building_tree.rb

Licensing

MIT (see COPYING.txt)