Transcription of Fibonacci Heaps - Princeton University
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Fibonacci Heaps - Princeton University
COS 423 Theory of Algorithms Kevin Wayne Spring 2007 Fibonacci HeapsLecture slides adapted from: Chapter 20 of Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein. Chapter 9 of The Design and Analysis of Algorithms by Dexter Starting from empty Fibonacci heap, any sequence ofa1 insert, a2 delete-min, and a3 decrease-key operations takesO(a1 + a2 log n + a3) n1log nnlog nlog n1 BinomialHeaplog nlog nlog nlog nlog nlog n1 FibonacciHeap 11log n11log n1 RelaxedHeap11log n11log n1 LinkedList1nn1nnis-empty11111 Priority Queues Performance Cost Summary amortizedn = number of elements in priority queue3 Hopeless challenge. O(1) insert, delete-min and decrease-key. Why?Priority Queues Performance Cost Summarymake-heapOperationinsertfind-mind elete-minuniondecrease-keydelete1 BinaryHeaplog n1log nnlog nlog n1 BinomialHeaplog nlog nlog nlog nlog nlog n1 FibonacciHeap 11log n11log n1 RelaxedHeap11log n11log n1 LinkedList1nn1nnis-empty11111 amortizedn = number of elements in priority queue4 Fibonacci HeapsHistory.
18 52 23 17 35 26 46 24 44 0123 min current rank 28 Fiboacci Heaps: Delete Min Delete min.! Delete min; meld its children into root list; update min.! Consolidate trees so that no two roots have same rank. 39 7 41 30 18 52 23 17 35 26 46 24 44 0123 min current rank link 41 into 18
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