Lecture19 - Algorithms in Systems Engineering IE170 Lecture...

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Unformatted text preview: Algorithms in Systems Engineering IE170 Lecture 19 Dr. Ted Ralphs IE170 Lecture 19 1 References for Todays Lecture Required reading CLRS Chapter 22-24 References R. Sedgewick, Algorithms in C++ (Third Edition), 1998. IE170 Lecture 19 2 Another View of Prims Algorithm Last time, we derived Prims Algorithm as a special case of graph search . The algorithm can also be viewed as a special case of another general class of algorithms called greedy algorithms . A greedy algorithm is one that makes the choice at each step that looks the best at the moment and doesnt reconsider that choice later. We can view the construction of an MST as a greedy algorithm, but first we must define some terminology. Given an undirected graph G = ( V, E ) , a cut is a set S V that defines a partition of V into two nonempty subsets, S and V \ S . An edge is said to cross the cut if it connects a node in S to a node in V \ S . Our goal is to build a spanning tree by adding one edge at a time to a set T in a greedy fashion. Basically, we just need to somehow guarantee ourselves that at each step, the current set can be extended to an MST . How do we do that? IE170 Lecture 19 3 Safe Edges Lets assume that our current set of edges T already satisfies the property that T can be extended to an MST . Question : What edges can we add to T to maintain the property?...
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This note was uploaded on 02/29/2008 for the course IE 170 taught by Professor Ralphs during the Spring '07 term at Lehigh University .

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Lecture19 - Algorithms in Systems Engineering IE170 Lecture...

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