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22 - Chapter 7.1 - The Maximum-Flow Problem and the Ford-Fulkerson Algorithm

# 22 - Chapter 7.1 - The Maximum-Flow Problem and the Ford-Fulkerson Algorithm

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2/22 - Chapter 7.1 - The Maximum-Flo... Graphs to model transportation networks - networks whose edges carry some sort of tra ff٠ c and whose nodes act as “switches” passing tra ff٠ c between di erent edges a highway system - edges are highways, nodes are interchanges fluid network - edges are pipes that carry liquid, nodes are junctures where pipes are plugged together Ingredients: capacities on edges indicate how much they can carry source nodes generate tra ff٠ c sink (or destination) nodes can “absorb” tra ff٠ c as it arrives tra ff٠ c which is transmitted across the edges Flow Networks flow = tra ff٠ c, an abstract entity that is generated at source nodes, transmitted across edges, and absorbed at sink nodes

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Unformatted text preview: a directed graph G = (V, E) with the following features Associated with each edge is a capacity, a nonnegative number, c e There is a single source node s ∈ V There is a single sink node t ∈ V Nodes other than s and t = internal nodes Assumptions No edge enters the source s and no edge leaves the sink t there is at least one edge incident to each node all capacities are integers 60-1 60 Defning Flow An s-t ±ow is a ²unction ² that maps each edge e to a nonnegative real number, ² : E -> R + ; the value ²(e) intuitively represents the amount o² ±ow carried by an edge e A ±ow must satis²y the ²ollowing two properties: 60-2...
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22 - Chapter 7.1 - The Maximum-Flow Problem and the Ford-Fulkerson Algorithm

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