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Fibonacci Heap paper and implementation in Python for the course: Algorithm Construction and Analysis 2

License: MIT License

Python 48.40% Makefile 0.39% TeX 51.20%
python python3 data-structures heap fibonacci-heap fibonacci algorithms-datastructures

fheap's Introduction

fheap

Fibonacci Heap implementation in Python for the course: Algorithms Construction and Analysis 2.

The paper we wrote (in Serbian) can be read here.

About Fibonacci heaps

In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. Michael L. Fredman and Robert E. Tarjan developed Fibonacci heaps in 1984 and published them in a scientific journal in 1987. Fibonacci heaps are named after the Fibonacci numbers, which are used in their running time analysis. Using Fibonacci heaps for priority queues improves the asymptotic running time of important algorithms, such as Dijkstra's algorithm for computing the shortest path between two nodes in a graph, compared to the same algorithm using other slower priority queue data structures. Source: Wikipedia

More information can be obtained from the original paper or from the following slides.

Complexity comparison (theoretical)

Operation Binary heap Fibonacci heap
find_min() O(1) O(1)
extract_min() O(log n) O(log n)
insert(v) O(log n) O(1)
decrease_key(k, v) O(log n) O(1)
merge(h) O(n) O(1)

Usage

See the test file for more detailed examples.

f = FibonacciHeap()

f.insert(10)
f.insert(2)
f.insert(50)
f.insert(5)

f.print()

print(f.extract_minimum())

print(f.find_minimum())

f2 = FibonacciHeap()
f2.insert(12)
f2.insert(222)
f2.insert(54)

f.merge(f2)
f.print()

f.decrease_key(f.root_list.right.right, 1)
f.print()

f.delete(f.root_list.right)
f.print()

Performance comparison

TODO

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