Lecture14

Lecture14 - Complexity Kruskal's Algorithm T is the set of...

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IE 495 Lecture 14 October 17, 2000

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Reading for This Lecture Primary Horowitz and Sahni, Chapter 4 Kozen, Lecture 3 Secondary Miller and Boxer, Chapter 12 (up to page 286)
Spanning Trees We are given a graph G = ( V, E ). A spanning tree of E is a maximal acyclic subgraph ( V, T) of G. A spanning tree always has | V | -1 edges (why?).

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Minimum Spanning Tree We associate a weight w e with each edge e . Objective : Find a spanning tree of minimum weight. Applications
Prim's Algorithm S is the set of nodes in the tree S = {0} for (i = 1; i < n; i++){ SELECT v S nearest to S; S = UNION(S, v); }

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Analysis of Prim's Algorithm Correctness Optimality Implementation

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Unformatted text preview: Complexity Kruskal's Algorithm T is the set of edges in the tree T = for (i = 0; i < m; i++){ SELECT the cheapest edge e if (feasible(UNION(T, e)){ UNION(T, e); } Analysis of Kruskal's Algorithm Correctness Optimality Implementation Complexity Parallel MST Prim's Algorithm Each processor is responsible for a subset of the nodes. Implementation Analysis Baruvka's Algorithm At each step, select all edges that connect some component of the graph to it's nearest neighbor. Add all these edges to the tree simultaneously. Why does this work? Sequential Implementation...
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This note was uploaded on 08/06/2008 for the course IE 495 taught by Professor Linderoth during the Fall '08 term at Lehigh University .

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Lecture14 - Complexity Kruskal's Algorithm T is the set of...

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