Lecture10

# Lecture10 - Graphs and Network Flows ISE 411 Lecture 10 Dr...

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Graphs and Network Flows ISE 411 Lecture 10 Dr. Ted Ralphs

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ISE 411 Lecture 10 1 References for Today’s Lecture Required reading Sections 21.3 References AMO Chapter 5 CLRS Chapter 25
ISE 411 Lecture 10 2 Shortest Path Algorithms Special structure easy! Special topology : Reaching Algorithm Special cost structure : Dijkstra’s Algorithm General network with negative cycles much harder! Identify a negative cycle if one exists OR Solve the problem if no negative cycle exists

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ISE 411 Lecture 10 3 General Label-Correcting Algorithms Maintain a distance label d ( j ) for all nodes j N If d ( j ) is infinite, the algorithm has not found a path joining the source node to node j . If d ( j ) is finite, it is the distance from the source node to that node along some path (upper bound). No label is permanent until the algorithm terminates.
ISE 411 Lecture 10 4 Optimality Conditions Theorem 1. [5.1] For every node j N , let d ( j ) denote the length of

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• Spring '14
• TedRalphs
• Graph Theory, Shortest path problem, shortest path, shortest path distances, Dr. Ted Ralphs

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