Lecture13

# Lecture13 - Graphs and Network Flows IE411 Lecture 13 Dr...

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Graphs and Network Flows IE411 Lecture 13 Dr. Ted Ralphs

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IE411 Lecture 13 1 References for Today’s Lecture
IE411 Lecture 13 2 References for Today’s Lecture Required reading Sections 21.1–21.2 References AMO Chapter 6 CLRS Sections 26.1–26.2

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IE411 Lecture 13 3 Labeling Algorithm (Ford and Fulkerson (1956)) Fill in details of generic augmenting path algorithm how to identify augmenting path (or show no path exists) whether algorithm terminates in finite number of iterations whether final flow value is maximal The labeling algorithm is the most straightforward variant. The cost to find the augmenting path is low, but the number of augmnentations can be high. Depth-first search is a special case.
IE411 Lecture 13 4 Identifying an Augmenting Path Use search technique to find a directed path in G ( x ) from s to t At any step, partition nodes into labeled and unlabeled Iteratively select a labeled node and scan its arc adjacency list in G ( x ) to reach and label additional nodes When sink becomes labeled, augment flow, erase labels and repeat Terminate when all labeled nodes have been scanned and sink remains unlabeled

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IE411 Lecture 13 5 Labeling Algorithm Input: A network G = ( N, A ) and a vector of capacities u Z A Output: x represents the maximum flow from node s to node t label node t while t is labeled
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• Spring '14
• TedRalphs
• Graph Theory, Flow network, Maximum flow problem, Max-flow min-cut theorem, lower bounds, Integrality Theorem

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