# Ruby extension implementing a priority queue

## Description This is a fibonacci-heap priority-queue implementation. That means

insert:                      O(1)
decrease_priority: Amortized O(1)
delete_min:        Amortized O(log n)

This project is different from K. Kodamas PQueue in that it allows a decrease key operation. That makes PriorityQueue usable for algorithms like dijkstras shortest path algorithm, while PQueue is more suitable for Heapsort and the like.

## Legal stuff (c) 2005 Brian Schr?der

Please submit bugreports to priority_queue@brian-schroeder.de

This extension is under the same license as ruby.

Do not hold me reliable for anything that happens to you, your programs or anything else because of this extension. It worked for me, but there is no guarantee it will work for you.

## Requirements

* Ruby 1.8
* c Compiler

## Installation

### Installing from source

De-compress archive and enter its top directory. Then type:

($ su)
 # ruby setup.rb

These simple step installs this program under the default location of Ruby libraries. You can also install files into your favorite directory by supplying setup.rb some options. Try "ruby setup.rb --help".

### Installing a ruby gem

($ su)
 # gem install PriorityQueue

## Usage

In this priority queue implementation the queue behaves similarly to a hash that maps objects onto priorities.

### Hash Interface

require 'priority_queue'

q = PriorityQueue.new
q["node1"] = 0
q["node2"] = 1
q.min #=> "node1"
q[q.min] #=> 0
q.min_value #=> 0

q["node2"] = -1
q.delete_min #=> "node2", 1
q["node2"] #= nil
q["node3"] = 1

q.delete("node3") #=> "node3", 1
q.delete("node2") #=> nil

### Queue Interface

require 'priority_queue'

q = PriorityQueue.new
q.push "node1", 0 
q.push "node2", 1

q.min #=> "node1"

q.decrease_priority("node2", -1)

q.pop_min #=> "node2"
q.min     #=> "node1"

for more exmples look into the documentation, the unit tests and the benchmark suite.

### Dijkstras shortest path algorithm

def dijkstra(start_node)
  # Nodes that may have neighbours wich can be relaxed further
  active = PriorityQueue.new         
  # Best distances found so far
  distances = Hash.new { 1.0 / 0.0 } 
  # Parent pointers describing shortest paths for all nodes
  parents = Hash.new                 

  # Initialize with start node
  active[start_node] = 0
  until active.empty?

u, distance = active.delete_min distances = distance d = distance + 1 u.neighbours.each do | v | next unless d < distances # we can't relax this one active = distances = d parents = u end


## Performance The benchmark directory contains an example where a random graph is created and the shortests paths from a random node in this graph to all other nodes are calculated with dijkstras shortests path algorithm. The algorithm is used to compare the three different priority queue implementations in this package.

* PoorPriorityQueue: A minimal priority queue implementation wich has
  delete_min in O(n).
* RubyPriorityQueue: An efficent implementation in pure ruby.
* CPriorityQueue: The same efficent implementation as a c extension.

The results are shown here

![Runtime for graphs of up to 8_000 Nodes](doc/compare_small.png "Runtime for graphs of up to 8_000 Nodes")

![Runtime for graphs of up to 600_000 Nodes](doc/compare_big.png "Runtime for graphs of up to 600_000 Nodes")

## Todo

* Only write documentation once