L06-maxflow - Maximum flow sender receiver Lecture6:Jan25...

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1 Maximum flow sender receiver Capacity constraint Lecture 6: Jan 25
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2 Network transmission Given a directed graph G A source node s A sink node t Goal: To send as much information from s to t
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3 Flows An s-t flow is a function f which satisfies: (capacity constraint) (conservation of flows) (conservation of flows ( at intermediate vertices )
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4 Value of the flow s t   10     10   9   8   4   10     10   6   2 10 3 9 9 9 10 7 0  G: 6 Value = 19 Maximum flow problem: maximize this value
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5 Flow decomposition Any flow can be decomposed into at most m flow paths. The same idea applies to the Chinese postman problem
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6 An upper bound sender receiver
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7 Cuts An s-t cut is a set of edges whose removal disconnect s and t The capacity of a cut is defined as the sum of the capacity of the edges in the cut Minimum s-t cut problem: minimize this capacity of a s-t cut
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8 Flows ≤ cuts Let C be a cut and S be the connected component of G-C containing s. Then:
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L06-maxflow - Maximum flow sender receiver Lecture6:Jan25...

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