class_7_flow_networks(4).pdf

# class_7_flow_networks(4).pdf - Flow networks Flow networks...

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Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks August 2, 2017

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Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Overview 1 Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications
Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks A Flow networks is a directed graph with a pair of special vertices s (source) and t (sink), in which each edge ( u , v ) E has a non-negative capacity c ( u , v ). The capacity of each edge is given by a function: c : E R 0 Our goal is to find a maximal flow from s to t such that in each edge ( u , v ) E we have at most ” c ( u , v ) flow”.

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Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks A Flow networks is a directed graph with a pair of special vertices s (source) and t (sink), in which each edge ( u , v ) E has a non-negative capacity c ( u , v ). The capacity of each edge is given by a function: c : E R 0 Our goal is to find a maximal flow from s to t such that in each edge ( u , v ) E we have at most ” c ( u , v ) flow”.
Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Example We might imagine a network of roads between cities, such that each road can allow some given number of cars per hour and we want to maximize the number of cars going from the city s to the city t .

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Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks Our goal is to find a maximal flow from s to t such that in each edge ( u , v ) E we have at most ” c ( u , v ) flow”.
Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks Our goal is to find a maximal flow from s to t such that in each edge ( u , v ) E we have at most ” c ( u , v ) flow”.

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Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks Our goal is to find a maximal flow from s to t such that in each edge ( u , v ) E we have at most ” c ( u , v ) flow”.
Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks Our goal is to find a maximal flow from s to t such that in each edge ( u , v ) E we have at most ” c ( u , v ) flow”.

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Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF Edmonds-Karp algorithm Applications Flow networks For a vertex u V we will denote T - ( u ) = { w V | ( w , u ) E } And, we will denote T + ( u ) = { w V | ( u , w ) E }
Flow networks Flow networks Definition of a flow The value of a flow Ford-Fulkerson MCMF

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• Fall '12
• Algorithms, Flow network, Maximum flow problem, Max-flow min-cut theorem, Network flow, εF

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