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1
Maximum flow
sender
receiver
Capacity constraint
Lecture 6: Jan 25
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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
3
Flows
An st flow is a function f which satisfies:
(capacity constraint)
(conservation of flows)
(conservation of flows
(
at intermediate vertices
)
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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
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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An upper bound
sender
receiver
7
Cuts
An
st
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
st
cut problem:
minimize this capacity of a
st
cut
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Flows ≤ cuts
Let
C
be a cut and
S
be the connected component of
GC
containing
s.
Then:
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This note was uploaded on 10/13/2009 for the course CS 5150 taught by Professor Xulei during the Spring '09 term at University of Central Arkansas.
 Spring '09
 xulei

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