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# lecture11 - e62: lecture 11 20/10/10 Vertex Integrality •...

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Unformatted text preview: e62: lecture 11 20/10/10 Vertex Integrality • Min-cost-fow problem • Thm: IF capacities and production/consumption amounts are integer-valued then every vertex is integer-valued • ¡acilitates solution oF discrete optimization problems • Many discrete optimization problems are NP-hard • But not those that we will treat using fow optimization 1 min ( i,j ) ∈ E c ij f ij s . t . ∑ k ( j,k ) ∈ E f jk- ∑ i ( i,j ) ∈ E f ij = b j ≤ f ij ≤ u ij e62: lecture 11 20/10/10 Matching Problems • Grooms = sources • Brides = sinks • ¡low optimization 2 grooms brides c ij = if compatible 1 if incompatible min ∑ ( i,j ) ∈ E c ij f ij s . t . ∑ { k | ( j,k ) ∈ E } f jk = 1 ∑ { i | ( i,j ) ∈ E } f ij = 1 f ij ∈ { , 1 } min ∑ ( i,j ) ∈ E c ij f ij s . t . ∑ { k | ( j,k ) ∈ E } f jk = 1 ∑ { i | ( i,j ) ∈ E } f ij = 1 ≤ f ij ≤ 1 e62: lecture 11 20/10/10 Shortest Path and Transportation Problems • Origin = source • Destination = sink • ¡low optimization...
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## This note was uploaded on 07/29/2011 for the course MS&E 111 at Stanford.

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lecture11 - e62: lecture 11 20/10/10 Vertex Integrality •...

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