'Minimum cost spanning tree' presentation slideshows

Minimum Spanning Trees

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Algorithms and Complexity

Algorithms and Complexity. The sphere of algorithmic problems. ?. 5. 2. 3. B. ?. 1. 4. 2. 2. 3. 2. C. D. 6. Traveling Salesman Problem (TSP): find the shortest route that passes though each of the nodes in a graph exactly once and returns to the starting node. starting point.

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First-Cut Techniques

First-Cut Techniques. Lecturer: Jing Liu Email: neouma@mail.xidian.edu.cn Homepage: http://see.xidian.edu.cn/faculty/liujing Xidian Homepage: http://web.xidian.edu.cn/liujing. First-Cut Techniques. The Greedy Approach Graph Traversal.

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22c:31 Algorithms

22c:31 Algorithms. Minimum-cost Spanning Tree (MST). Minimum-Cost Spanning Tree. weighted connected undirected graph spanning tree cost of spanning tree is sum of edge costs find spanning tree that has minimum cost. 8. 10. 14. 1. 3. 5. 7. 3. 7. 12. 6. 4. 2. 2. 4. 6. 8. 9.

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???. ??. Graph. ????. 5-1 ?????. 5-2 ????????? ?????????. 5-3 ????? ?????????. 5-4 ??? ( Spanning Tree ) Kruskal ???? Prim ???. 5-5 ???? ( Shortest Path ) Dijkstra ???? Floyd ???. 5-6 ???? ( Topological Sorting ). 5- 7 ???? ( Critical Path ). 5-1 ?????. a. a. e. b.

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WEIGHTED GRAPHS

WEIGHTED GRAPHS. Weighted Graphs. Graph G = (V,E) such that there are weights/costs associated with each edge w((a,b)): cost of edge (a,b) representation: matrix entries <-> costs. a. 20. 35. e. b. 12. 32. c. 65. d. Problems on Weighted Graphs. Minimum-cost Spanning Tree

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Introduction to Graph Theory

Introduction to Graph Theory. Lecture 06: Properties of Trees and Minimum Spanning Trees. Definition of a Tree. Tree is a connected acyclic graph i.e. Connected and containing no cycle Have you come across trees before? What classes of trees have we seen so far?. 1. 2. 1. 2. 3. 3.

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Minimum Spanning Tree

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Graphs

Graphs. Definitions. A graph is two sets. A set of nodes or vertices V A set of edges E Edges connect nodes. The number of vertices | V | The number of edges | E | A sparse graph is one with relatively few edges A dense graph is one with relatively many edges

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