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lec14

# lec14 - Fibonacci Heaps Insert Actual O(1 Amortized O(1...

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Fibonacci Heaps Actual Amortized Insert O(1) O(1) Remove min (or max) O(n) O(log n) Meld O(1) O(1) Remove O(n) O(log n) Decrease key (or increase) O(n) O(1)

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Single Source All Destinations Shortest Paths 1 2 3 4 5 6 7 2 6 16 7 8 10 3 14 4 4 5 3 1
Greedy Single Source All Destinations Known as Dijkstra’s algorithm. Let d(i) be the length of a shortest one edge extension of an already generated shortest path, the one edge extension ends at vertex i . The next shortest path is to an as yet unreached vertex for which the d() value is least. After the next shortest path is generated, some d() values are updated (decreased).

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Greedy Single Source All Destinations 1 2 3 4 5 6 7 2 6 16 7 8 10 3 14 4 4 5 3 1 Path Length 1 0 1 3 2 1 3 5 5 1 2 6 1 3 9 5 4 1 3 10 6 1 3 11 6 7
Operations On d() Remove min. Done O(n) times, where n is the number of vertices in the graph. Decrease d() . Done O(e) times, where e is the number of edges in the graph.

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• Spring '10
• sartajsahani
• Graph Theory, Fibonacci heap, overall complexity, theNode, top-level list

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