Lazy priority queue

Lazy priority queue is a pure Ruby priority queue which implements a lazy binomial heap. It supports the change priority operation, being suitable for algorithms like Dijkstra's shortest path and Prim's minimum spanning tree. It can be instantiated as a min-priority queue as well as a max-priority queue.

With RubyGems:

$ gem install 'lazy_priority_queue'

First instantiate a priority queue.

require 'lazy_priority_queue'

queue = MinPriorityQueue.new

There is also a MaxPriorityQueue class.

Use push(element, priority) to insert an element with a given priority to the queue.

queue.push :a, 1  # => :a
queue.push :b, 2  # => :b
queue.push :c, 3  # => :c

min() will retrieve the minimum priority element without removing it from the queue; analogously, use max() in case of a max-priority queue.

queue.min  # => :a

decrease_key(element, new_priority) decreases an element's priority (trying to increase it will raise an error). For a max-priority queue, increase_key(element, new_priority) modifies a priority (but will not be able to decrease it).

queue.decrease_key :c, 0  # => :c

Use pop() to extract the minimum priority element from the queue; or maximum, given a max-priority queue.

queue.pop  # => :c
queue.pop  # => :a
queue.pop  # => :b

Finally, there are these additional instance methods: delete(element), size and empty?.

A lazy binomial heap has these times:

It is worth noting that a Fibonacci heap has better amortized time for change priority, O(1) namely, theoretically providing better performance for priority queues. On the other side, nodes in this kind of heap stores more pointers to other nodes than their binomial heap fellows, making it a more memory consuming data structure. Hence in practice the time spent allocating memory drawbacks Fibonacci heap behind binomial heap as seen in the next section.

All the following libraries underwent 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. See test/performance.rb for details.

Lazy priority queue is recommended if you are seeking a pure Ruby implementation of a priority queue capable (or not) of modifying the priority of its elements. Otherwise, in the field of low-level extended Ruby, supertinou's PriorityQueue is the right choice; and if you do not need changing priorities at all, PriorityQueueCxx is the one.

Pure Ruby | Fibonacci heap | Elements are identified by their priority: change priority is not supported except through a hack.

Lazy priority queue —which is based on a lazy binomial heap— performed 2 times better than Algorithms. Issue kanwei/algorithms#23 motivated the writing of this library.

Pure Ruby | Sorted array | Does not support change priority.

PQueue was not as fast as the others. Anyway, it is a really simple implementation that would sort a reduced number of elements satisfactorily.

C++ extension | Sorted array | Does not support change priority.

PriorityQueueCxx, wrapping the C++ standard library implementation, is the fastest priority queue for Ruby out there.

C extension | Fibonacci heap | Supports change priority.

supertinou/PriorityQueue outperforms Lazy priority queue.

Pure Ruby | Unsorted array | Does not support change priority.

ninjudd/PriorityQueue did not complete the task in a reasonable amount of time.

These two lectures on data structures were helpful for writing this library:

• http://web.stanford.edu/class/cs166/lectures/06/Slides06.pdf
• http://web.stanford.edu/class/cs166/lectures/07/Slides07.pdf

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