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	Fibonacci heap -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		A Fibonacci heap can be used to improve the running time of (Click link for more info and facts about Dijkstra's algorithm) Dijkstra's algorithm for computing shortest paths in a graph and (Click link for more info and facts about Prim's algorithm) Prim's algorithm for computing a minimum spanning tree of a graph.
		The name of Fibonacci heap comes from (A number in the Fibonacci sequence) Fibonacci numbers which are used in the running time analysis.
		Fibonacci heaps were discovered by Michael L. Fredman and (Click link for more info and facts about Robert E. Tarjan) Robert E. Tarjan in 1984 and first published in a scientific journal in 1987.
	www.absoluteastronomy.com /encyclopedia/f/fi/fibonacci_heap.htm (1399 words)

	Fibonacci heap - Wikipedia, the free encyclopedia
		A Fibonacci heap can be used to improve the running time of Dijkstra's algorithm for computing shortest paths in a graph and Prim's algorithm for computing a minimum spanning tree of a graph.
		A Fibonacci heap is a collection of trees satisfying the minimum-heap property, that is, the key of a child is always greater than or equal to the key of the parent.
		Fibonacci heaps were developed by Michael L. Fredman and Robert E. Tarjan in 1984 and first published in a scientific journal in 1987.
	en.wikipedia.org /wiki/Fibonacci_heap (1507 words)

	Binary heap - Wikipedia, the free encyclopedia
		Heaps where the comparison function is mathematical "greater than" are called max-heaps; those where the comparison function is mathematical "less than" are called "min-heaps".
		Note that the ordering of siblings in a heap is not specified by the heap property, so the two children of a parent can be freely interchanged (as long as this does not violate the shape property).
		We can do this in O(log n) time, using a binary heap, by adding the element on the bottom level of the heap regardless, then considering the added element and its parent and swapping the element and its parent if need be until we are assured the heap property remains.
	en.wikipedia.org /wiki/Binary_heap (970 words)

	[No title]
		Binomial Heap A binomial heap is a set of binomial trees that satisfies the binomial heap properties: Each tree is heap ordered: the key of a node is greater than or equal to the key of its parent.
		The trees in a fibonacci heap are not constrained to be binomial trees.
		The fibonacci heap is a data structure that performs all the basic heap operations in O(1) amortized time except extract-min and delete which take O(log n) amortized time.
	people.bu.edu /somag/LecNov6.doc (852 words)

	Amof:Info on Fibonacci Sequences
		The Fibonacci sequence is a recursive sequence where the first two values are 1 and each successive term is obtained by adding together the two previous terms.
		Fibonacci Quarterly is a mathematical periodical devoted entirely to the subject of mathematics related to Fibonacci sequences.
		In the area of physics, there are indications that the golden ratio and Fibonacci numbers are related to the structure of atoms and also to the spacing of planets in the solar system.
	theory.cs.uvic.ca /~cos/amof/e_fiboI.htm (1880 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		* nodes - An array of pointers to nodes in the heap.
		This allows any type heap to be given as an * argument to a particular algorithm.
		It is up to the user to ensure the * correct heap type is passed to the given functions.
	www.cosc.canterbury.ac.nz /tad.takaoka/alg/heaps/fheap.h (623 words)

	Citations: Relaxed heaps: An alternative to Fibonacci heaps with applications to parallel computation - Driscoll, ... (Site not responding. Last check: 2007-10-08)
		Runrelaxed heaps support all operations within the same time bounds as Fibonacci heaps but in the worst case except meld, which takes O(log n) worst case time.
		Fibonacci and rank relaxed heaps (we did not implement run relaxed heaps, which su er from much larger overhead than rank relaxed heaps) o er the largest number of choices.
		Fibonacci and rank relaxed heaps (we did not implement run relaxed heaps, which can be seen to suffer from much larger overhead than rank relaxed heaps) offer the largest number of choices.
	citeseer.ist.psu.edu /context/128628/0 (3237 words)

	Algorithm Repository Home Page (Site not responding. Last check: 2007-10-08)
		[Binary Heap, Fibonacci Heap, 2-3 Heap, Trinomial Heap]
		The heap implementation of Dijkstra's algorithm is an example of this.
		The trees in a 2-3 heap can be viewed in two different ways, and this leads to two different 2-3 heap implementations.
	www.cosc.canterbury.ac.nz /~tad/alg/heaps/heaps.html (184 words)

	420 Review 1
		Binary Heap: A complete, partially ordered binary tree (the value in each internal node is less or equal to the values of its children).
		The Binomial heap is thus a PRIORITY QUEUE.
		Fibonacci Heap: A lazy binomial heap in which consolidation is delayed until delete-min, thus a priority queue with better amortized running time.
	www.wam.umd.edu /~jtyler/420finalreview.html (2718 words)

	[No title]
		We were interested in the binomial heap (a mergeable heap) because Union() is effected in lg n time; in an amortized analysis, Union() is effected in constant time with the Fibonacci Heap, primarily because the "work" of heap maintenance is "put off" until the Extract-Min() operation is needed.
		The subject of mergeable heaps is categorized under the topic of disjoint sets; the issue is the maintenance of information in sets that can grow independently but that will be dynamically merged.
		Binomial and Fibonacci heaps are examples of such disjoint sets, but with additional useful properties (constraints) that deal with the arrangement of keys in a "heap" ordering.
	ranger.uta.edu /~cook/aa/transcript/ln13-14f (1372 words)

	TUTORIAL (Site not responding. Last check: 2007-10-08)
		However, the trees in a Fibonacci Heap are not constrained to be binomial trees.
		A given Fibonacci Heap H is accessed by a pointer min[h] to the root of the tree containing a minimum key; this node is called the minimum node of the Fibonacci heap.
		The roots of all the trees in a Fibonacci heap are linked together using their left and right pointers into a circular, doubly linked list called the root list of the Fibonacci Heap.
	sili.adnu.edu.ph /~rolladiv/teaching/resources/heap/tutor2.html (420 words)

	fibonacci heaps (Site not responding. Last check: 2007-10-08)
		The Fibonacci heaps are a complex structure, that provide the heap functions in a cheaper cost.
		The fibonacci heap has a circled Linked list of trees in its Root level, each of them is having a connected linked list of children etc...
		Each node in the fibonacci heap has pointer for his parent, his left and right siblings, pointer to the linked list of children as well as a void pointer for the data field, it also has a colour bit, and a integer with the number of children's it got.
	www.math.tau.ac.il /~scipio/UN/plgraph/fib.html (145 words)

	Part 1 Command Modifications (Site not responding. Last check: 2007-10-08)
		So, the min element of the Fibonacci heap (of name1) will be removed and then inserted to the inventory of the second argument.
		We will be testing each individual binomial heap for the heap property.
		It will allow us to verify that your fibonacci heap satisfies the constraints for such structures, regardless of the specific ordering of values in the f-heap.
	www.cs.umd.edu /class/spring2004/cmsc420/sp04-part2v1/node35.html (642 words)

	Solutions to homework #4 (Site not responding. Last check: 2007-10-08)
		When an element (binomial tree of order 0) is inserted into a binomial heap which already contains a tree of order 0, the merging of tree pairs occurs until there are no longer two binomial trees of the same order in the heap.
		A Fibonacci heap which supports only the mergeable heap operations (Insert, Merge, DeleteMin) is a collection of unordered binomial trees.
		Decreasing key of the small child of the root causes it to be "on its own", beside the skewed tree of n nodes, thus maintaining the invariant "Fibonacci Heap with one skewed tree and one trivial tree".
	www.cs.uoregon.edu /~andrzej/315S98/hw4sols.html (640 words)

	[No title]
		Using amortized analysis, the asymptotically fastest heap 00017 // data structure is the Fibonacci heap.
		The constants are a little 00018 // high so the real speed gain will not be seen until larger data sets 00019 // are required, but in most cases, if the data set is small, then the 00020 // run-time will be neglible anyway.
		For assignment, the function 00038 // FHN_Assign() should be called before code that deals with the copy of 00039 // the key value.
	rioja.sangria.cs.cmu.edu /tumble/doc/fibheap_8C-source.html (1182 words)

	[No title]
		The amortization refers to the "distribution" of the computational cost accross the set of Fibonacci Heap operations.
		It's pretty strightforward to see that considering amortized running time for the operation on Trivial Heaps is equivalent to worst-case running time (that will become obvious when we explain how we can achieve these time bounds).
		As a proof, we'll give an actual construction of the Fibonacci heap, consisting of only this tree.
	www.cs.cmu.edu /afs/cs.cmu.edu/academic/class/15750-s04/www/HW3_sol.txt (674 words)

	[No title]
		The class of binary heaps is a subset of the class of binary trees.
		The two heaps pictured above would have the following representations as arrays: (2, 4, 5, 7, 11, 6, 8, 9, 10, 12) (1, 2, 6, 3, 5, 7) The first element of the array, at index 1, is the heap's root.
		A Fibonacci heap is a complicated data structure, quite a bit more involved to explain than a simple binary heap.
	www.stanford.edu /~blp/uniformity/uniformity-2001.04.27.text (9609 words)

	fib (Site not responding. Last check: 2007-10-08)
		A Fibonacci Heap is a very efficient heap.
		The way the fibonacci heap obtains this is by delaying the organizing of the items until you extract.
		The type of heap you create depends upon which make heap function you call.
	resnet.uoregon.edu /~gurney_j/jmpc/fib.html (271 words)

	Algorithms for Binomial and Fibonacci Heaps (Site not responding. Last check: 2007-10-08)
		For this implementation of binomial and Fibonacci heaps, the children of a binomial tree node are linked in a circular list.
		Binomial trees are linked in a circular list to form a binomial heap or Fibonacci heap.
		BinomialTree treeList - This is the lowest degree tree in the the binomial heap of this priority queue.
	www.d.umn.edu /~gshute/cs4521/ds/bin-fib.html (690 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Some graph problems, like minimum spanning tree and single-source-shortest-path problems call decrease-key much more often than other operations¡H.1 1´ó¨Fibonacci Heapsª ¨nLoosely based on binomial heaps If Decrease-key and Delete are never called, each tree is like a binomial tree¡6o# 4ó¨Fibonacci Heapsª ¨;A Fibonacci heap is a collection of heap-ordered trees.
		Each node x has pointed p[x] to its parent & child [x] to one of its children Children are linked together in a doubly-linked circular list.
		Therefore, actual cost is O(c)¡.,Tó¨Change in Potential¨üLet H be original heap.
	www.cs.aucegypt.edu /~abdelbar/fibonacci.ppt (267 words)

	Fibonacci heap (Site not responding. Last check: 2007-10-08)
		Definition: A heap made of a forest of trees.
		The amortized cost of the operations create, insert a value, decrease a value, find minimum, and merge or join (meld) two heaps, is a constant Θ(1).
		Paul E. Black, "Fibonacci heap", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/fibonacciHeap.html (115 words)

	8-Puzzle Solver
		Next, I upgraded the open list to a Fibonacci heap and the closed list to an AVL tree.
		For a Fibonacci heap, insertions take constant time and extracting the minimum takes O(lg n) time.
		The Fibonacci heap alone was an improvement, but it was not a drastic change.
	www.brian-borowski.com /Puzzle/Puzzle.html (541 words)

	heap (Site not responding. Last check: 2007-10-08)
		Definition: A complete tree where every node has a key more extreme (greater or less) than or equal to the key of its parent.
		binary heap, k-ary heap, binomial heap, Fibonacci heap.
		Chris L. Kuszmaul, "heap", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/heap.html (123 words)

	Diary for jmg
		I'm surprised that the Fibonacci heap code is just over 2k in size which considering what it does is really quite small.
		The fibonacci heap code is going well, I have been alerted to a couple more bugs dealing w/ pointers not being cleared after they no longer reference data.
		If you're knowledgable enough to actually look for a Fibonacci heap, you shouldn't have any need to be told what fh_extractmin does.
	www.advogato.org /person/jmg/diary.html?start=11 (3445 words)

	[No title]
		-->A templated implimentation of a fibonacci heap, derived from the abstract FibHeap.
		A templated implimentation of a fibonacci heap, derived from the abstract FibHeap.
		References FibHeap::DecreaseKey(), FHeap< Data >::heap, FibHeap::Insert(), FHeap< Data >::next_idx, FHeap< Data >::node_idx, FHeap< Data >::nodes, OK, and FHeap< Data >::size.
	rioja.sangria.cs.cmu.edu /tumble/doc/classFHeap.html (166 words)

	[No title]
		O(nlog n + e) overall complexity.¡¶ '" ªP- óÛ¨Min Fibonacci Heapª ¨BCollection of min trees.
		Set to false by remove min, which is the only operation that makes one node a child of another.
		Undefined for a root node.¡”+Z2ZZZ ZÈZ+ È ª Èóà ¨Fibonacci Heap Representationª ª óÞ¨Remove(theNode)ª¨ÊtheNode points to the Fibonacci heap node that contains the element that is to be removed.
	www.cise.ufl.edu /~sahni/cop5536/powerpoint/lec14.ppt (353 words)

	Journal of ambs (3914)
		The only place that I have used linked lists in perl [in code that actually gets used] is internally within the Fibonacci heap module.
		The Fibonacci heap gets defined later in the same chapter, and used later in the book to find minimum spanning tree (with Prim's algorithm) and shortest path - these graph algorithms, when used on large graphs, really need the performance of the Fibonacci heap to work well.
		I've had enough used feedback to show that the heap module collection does get used bu other people too.
	use.perl.org /~ambs/journal/19695 (206 words)

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