Lecture17 - Algorithms in Systems Engineering IE170 Lecture...

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Algorithms in Systems Engineering IE170 Lecture 17 Dr. Ted Ralphs
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IE170 Lecture 17 1 References for Today’s Lecture Required reading CLRS Chapter 24 References R. Sedgewick, Algorithms in C++ (Third Edition), 1998.
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IE170 Lecture 17 2 Dijkstra’s Algorithm We will assume for now that the edge lengths are all positive. The idea of Dijkstra’s Algorithm is to perform a graph search, updating the shortest known path to each encountered vertex as the search evolves. Throughout the algorithm, we maintain a quantity d ( v ) for each node v , which represents the length of the shortest path found so far. We will call d ( v ) the current estimate for node v . We start by assigning d ( r ) = 0 for the source node and d ( v ) = for all other nodes v . The node v to be processed next is the unprocessed node for which d ( v ) is minimized. The processing step consists of updating the estimates for all the neighbors of v .
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IE170 Lecture 17 3 Algorithm Summary We are given a graph G = ( V, E )
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