In computer science, a Fibonacci heap is a data structure for priority queue operations. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. consisting of a collection of heap-ordered trees. Fibonacci heaps were originally explained to be an extension of binomial heaps.[1] 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.
The amortized times of all operations on Fibonacci heaps is constant, except delete-min., the find-minimum operation takes constant amortized time.[2] The insert and decrease key operations also work in constant amortized time.[3] Deleting an element (most often used in the special case of deleting the minimum element) works in amortized time, where is the size of the heap.[3] This means that starting from an empty data structure, any sequence of a insert and decrease-key operations and bdelete-min operations would take worst case time, where is the maximum heap size. In a binary or binomial heap, such a sequence of operations would take time. A Fibonacci heap is thus better than a binary or binomial heap when is smaller than by a non-constant factor. It is also possible to merge two Fibonacci heaps in constant amortized time, improving on the logarithmic merge time of a binomial heap, and improving on binary heaps which cannot handle merges efficiently.
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.
^Fredman, Michael L.; Tarjan, Robert Endre (1987-07-01). "Fibonacci heaps and their uses in improved network optimization algorithms". Journal of the ACM. 34 (3): 596–615. doi:10.1145/28869.28874. ISSN 0004-5411.
^Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2001) [1990]. "Chapter 20: Fibonacci Heaps". Introduction to Algorithms (2nd ed.). MIT Press and McGraw-Hill. pp. 476–497. ISBN 0-262-03293-7. Third edition p. 518.
^ abCite error: The named reference Fredman And Tarjan was invoked but never defined (see the help page).
structures including the binary heap and binomial heap. consisting of a collection of heap-ordered trees. Fibonacciheaps were originally explained to be...
strict Fibonacciheap is a priority queue data structure with low worst case time bounds. It matches the amortized time bounds of the Fibonacciheap in the...
the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacciheap data...
Robert Tarjan in 1986. Pairing heaps are heap-ordered multiway tree structures, and can be considered simplified Fibonacciheaps. They are considered a "robust...
A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues.: 162–163 The...
science, a binomial heap is a data structure that acts as a priority queue. It is an example of a mergeable heap (also called meldable heap), as it supports...
heaps" (PDF). SIAM J. Computing. 40 (6): 1463–1485. doi:10.1137/100785351. Fredman, Michael Lawrence; Tarjan, Robert E. (July 1987). "Fibonacciheaps...
Corporation. P-923. Fredman, Michael Lawrence; Tarjan, Robert E. (1984). Fibonacciheaps and their uses in improved network optimization algorithms. 25th Annual...
elements. Variants of the basic heap data structure such as pairing heaps or Fibonacciheaps can provide better bounds for some operations. Alternatively, when...
connected components algorithm, and co-inventor of both splay trees and Fibonacciheaps. Tarjan is currently the James S. McDonnell Distinguished University...
of the weak heap structure allow constant amortized time insertions and decrease-keys, matching the time for Fibonacciheaps. Weak heaps were introduced...
operations take O(log n) time. For insertions, this is slower than Fibonacciheaps, which support insertion in O(1) (constant) amortized time, and O(log...
implementation, others do exist. These are: Leftist heap Binomial heapFibonacciHeap Pairing heap Skew heap A. Gambin and A. Malinowski. 1998. Randomized Meldable...
Among his contributions to computer science are the development of the Fibonacciheap in a joint work with Robert Tarjan, the transdichotomous model of integer...
findmin(S): Get the element with minimum key in the soft heap Other heaps such as Fibonacciheaps achieve most of these bounds without any corruption, but cannot...
heaps" (PDF). SIAM J. Computing. 40 (6): 1463–1485. doi:10.1137/100785351. Fredman, Michael Lawrence; Tarjan, Robert E. (July 1987). "Fibonacciheaps...
feedback vertex set Ferguson–Forcade algorithm Fibonacci number Fibonacci search Fibonacci tree Fibonacciheap Find find kth least element finitary tree finite...
maintain the heap property. Examples of mergeable heap data structures include: Binomial heapFibonacciheap Leftist tree Pairing heap Skew heap A more complete...
heaps" (PDF). SIAM J. Computing. 40 (6): 1463–1485. doi:10.1137/100785351. Fredman, Michael Lawrence; Tarjan, Robert E. (July 1987). "Fibonacciheaps...
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