'Decrease key' presentation slideshows

Data Structures

Data Structures. Binary Heaps. Haim Kaplan & Uri Zwick December 2013. Required ADT. Maintain items with keys subject to Insert(x,Q) min(Q) Deletemin(Q) Decrease-key(x,Q, ? ) Delete(x,Q). Required ADT. Decrease-key(x,Q, ? ): Can simulate by Delete(x,Q), insert(x- ? ,Q).

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Chapter 24: Single-Source Shortest-Path

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CSCE 411 Design and Analysis of Algorithms

CSCE 411 Design and Analysis of Algorithms. Set 9: More Graph Algorithms Prof. Jennifer Welch Spring 2012. Generic MST Algorithm. input: weighted undirected graph G = (V,E,w) T := empty set while T is not yet a spanning tree of G

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Binomial heaps, Fibonacci heaps, and applications

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Fibonacci Heap

Fibonacci Heap. H. min. H .min. ( b). ( a). 23. 23. 7. 7. 3. 3. 17. 17. 24. 24. 26. 26. 46. 30. 30. 52. 52. 18. 18. 38. 38. 46. 35. 35. 39. 39. 41. 41. H. min. 23. 7. 3. 17. 24. ( a). 26. 30. 52. 18. 38. 46. 21. ( b). 23. 7. 3. 17. 24. 35. 39.

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Binomial heaps, Fibonacci heaps, and applications

Binomial heaps, Fibonacci heaps, and applications. Binomial trees. B 0. B 1. B i. B (i-1). B (i-1). Binomial trees. B i. B 0. B (i-1). B (i-2). B 1. Can prove by induction. Properties of binomial trees. 1) | B k | = 2 k. 2) degree(root(B k )) = k. 3) depth(B k ) = k.

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Fibonacci Heap

Fibonacci Heap. Fibonacci Heaps: A collection of heap-ordered trees. trees : rooted but unordered Each node x : P[x] points to its parent child[x] points to any one of its children,children of x are linked together in a circular doubly linked list

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2IL05 Data Structures

2IL05 Data Structures. Fall 2007 Lecture 13: Minimum Spanning Trees. Motivation. What is the cheapest network that connects a group of computers?. 1. 1. 2. 1. 1. 1. 3. 3. 0.5. 0.5. 12. 2. 3. 2. 3. 1. 1. 1. 1. 11. Minimum spanning graph.

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Single Source Shortest Paths

Single Source Shortest Paths. Definition Algorithms Bellman Ford DAG shortest path algorithm Dijkstra. Definition. Input Weighted, connected directed graph G=(V,E) Weight (length) function w on each edge e in E Source node s in V Task Compute a shortest path from s to all nodes in V.

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CISC220 Fall 2009 James Atlas

CISC220 Fall 2009 James Atlas. Nov 9: Heaps. Remaining Course Topics. Heaps Hashing Graphs. Heaps. Specialized Tree Often are Binary Heaps Satisfy Heap Property if B is a child node of A, then key(A) ? key(B) [in a Max-Heap]

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