PairingHeap

PairingHeap is a pure Ruby priority queue implementation using a pairing heap as the underlying data structure. While a pairing heap is asymptotically less efficient than the Fibonacci heap, it is usually faster in practice. This makes it a popular choice for Prim's MST or Dijkstra's algorithm implementations.

PairingHeap is currently being used as the priority queue data structure in RGL.

Also implementation without priority change support is provided(SimplePairingHeap), while the asymptotical complexity of the methods stay the same, bookkeeping of elements is not needed making, the constant smaller.

Installation

Add this line to your application's Gemfile:

gem 'pairing_heap'

And then execute:

$ bundle install

Or install it yourself as:

$ gem install pairing_heap

Documentation

https://rubydoc.info/gems/pairing_heap

Usage

require 'pairing_heap'

# Simple PairingHeap
simple_heap = PairingHeap::SimplePairingHeap.new
simple_heap.push(:a, 1)
simple_heap.push(:b, 2)
simple_heap.push(:c, 3)
simple_heap.peek # => :a
simple_heap.peek_priority # => 1
simple_heap.pop_with_priority # => [:a, 1]
simple_heap.pop # => :b

# Min priority queue
best_defenses = PairingHeap::MinPriorityQueue.new
best_defenses.push('Chelsea', 24)
best_defenses.push('City', 30)
best_defenses.push('Tottenham', 25)
best_defenses.any? # => true
best_defenses.size # => 3
best_defenses.decrease_key('City', 15)
best_defenses.min # => 'City'
best_defenses.pop # => 'City'
best_defenses.extract_min # => 'Chelsea'
best_defenses.extract_min # => 'Tottenham'
best_defenses.any? # => false

# Max priority queue
best_teams = PairingHeap::MaxPriorityQueue.new
best_teams.push('City', 56)
best_teams.push('United', 46)
best_teams.push('Leicester', 46)
best_teams.increase_key('Leicester', 47)
best_teams.max # => 'City'
best_teams.pop # => 'City'
best_teams.extract_max # => 'Leicester'

# Custom comparator(it defaults to :<=.to_proc)
compare_by_length = PairingHeap::PairingHeap.new { |l, r| l.length <= r.length }
compare_by_length.push(:a, '11')
compare_by_length.push(:b, '1')
compare_by_length.push(:c, '11')
compare_by_length.change_priority(:c, '')
compare_by_length.peek # => :c
compare_by_length.pop # => :c
compare_by_length.pop # => :b
compare_by_length.pop # => :a

# SafeChangePriortyQueue
queue = PairingHeap::SafeChangePriorityQueue.new
queue.push(:a, 1)
queue.push(:b, 2)
queue.change_priority(:a, 3) # This works and does not throw an exception
queue.peek # => :b

See also test/performance_dijkstra.rb for a Dijkstra algorithm implementation.

Changes from lazy_priority_queue

This API is a drop-in replacement of lazy_priority_queue with the following differences:

• Custom comparator provided to constructur, compares weights, not internal nodes
• change_priority returns self instead of the first argument
• enqueue returns self instead of the first argument
• Queue classes are in the PairingHeap namespace, so require 'pairing_heap does not load MinPriorityQueue to the global scope
• top_condition constructor argument is removed

Time Complexity

* Not available in SimplePairingHeap

Benchmarks

I picked the three fastest pure Ruby priority queue implementations I was aware of for the comparison:

• lazy_priority_queue that uses a lazy binomial heap. This is probably the most popular option. It was used in RGL until PairingHeap replaced it.
• Pure Ruby implementation of Fibonacci Heap from priority-queue (link to source)
• rb_heap that uses a binary heap. Note however that this implementation does not support change_priority operation.

All tests except for the third one were executed by benchmark-ips with parameters time = 60 and warmup = 15, on an Intel(R) Core(TM) i7-10700K CPU @ 3.80GHz.

Stress test without changing priority test(N = 1000) source code

Original performance test from lazy_priority_queue

A stress test of 1,000,000 operations: starting with 1,000 pushes/0 pops, following 999 pushes/1 pop, and so on till 0 pushes/1000 pops.

Stress test with changing priority(N = 1000) source code

A stress test of 1,501,500 operations: starting with 1,000 pushes/1000 change_priorities/0 pops, following 999 pushes/999 change_priorities/1 pop, and so on till 0 pushes/0 change_priorities/1000 pops.

Stress test with changing priority or push/pop(test ignored in summary) source code

Start with 500 pushes, then:

• If queue supports changing priority 500 change_priority calls, then 500 pops
• If does not support changing priority 500 push calls, then 1000 pops

Dijkstra's algorithm with RGL source code

Simple Dijkstra's algorithm implementation source code

Heaps that support change_priority operation use it. Heaps that do not support it use dijkstra implementation that do not rely on change_priority instead and do additional pops and pushes instead(see Dijkstra-NoDec from Priority Queues and Dijkstra’s Algorithm).

Summary

Change priority required

Change priority not required

Development

After checking out the repo, run bin/setup to install dependencies. Then, run rake test to run the tests. You can also run bin/console for an interactive prompt that will allow you to experiment.

To install this gem onto your local machine, run bundle exec rake install. To release a new version, update the version number in version.rb, and then run bundle exec rake release, which will create a git tag for the version, push git commits and the created tag, and push the .gem file to rubygems.org.

Contributing

Bug reports and pull requests are welcome on GitHub at https://github.com/mhib/pairing_heap.

License

The gem is available as open source under the terms of the MIT License.