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Unformatted text preview: DFS Review Topological Sort Strongly Connected Components IE170: Algorithms in Systems Engineering: Lecture 18 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University March 12, 2007 Jeff Linderoth IE170:Lecture 18 DFS Review Topological Sort Strongly Connected Components Taking Stock Last Time Topological Sort: Making the Perfect Martini Strongly Connected Components This Time: Uses of DFS Turn in Homework Now, please! Minimum Spanning Trees Jeff Linderoth IE170:Lecture 18 DFS Review Topological Sort Strongly Connected Components The Algorithm Theorems and Analysis Edge Classification A Canonical Problem A town as a set of houses and a set of potential roads Each each connects two and only two houses Constructing road from house u to house w costs w uv The Objective: Construct roads such that 1 Everyone is Connected 2 The total repair cost is minimum Jeff Linderoth IE170:Lecture 18 DFS Review Topological Sort Strongly Connected Components The Algorithm Theorems and Analysis Edge Classification Spanning Tree We model the problem as a graph problem. G = ( V,E ) is an undirected graph Weights w : E → R  E  w uv ∀ ( u,v ) ∈ E Find T ⊂ E such that 1 T connects all vertices 2 The weight w ( T ) def = ( u,v ) ∈ T w uv is minimized Jeff Linderoth IE170:Lecture 18 DFS Review Topological Sort Strongly Connected Components The Algorithm Theorems and Analysis Edge Classification Spanning TREE The notation T is not a coincidence. The set of edges T will form a tree . ( Why? ) This subset is known as a minimum spanning tree (MST) of G Jeff Linderoth IE170:Lecture 18 DFS Review Topological Sort Strongly Connected Components The Algorithm...
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This note was uploaded on 08/06/2008 for the course IE 170 taught by Professor Ralphs during the Spring '07 term at Lehigh University .
 Spring '07
 Ralphs
 Systems Engineering

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