Flow Decomposition theorem explanation
$begingroup$
I have a question about Flow Decomposition Theorem.
In the theorem say that a flow $f$ can be decompose in $k$ flows, $f_1, f_2 ... f_k$, and the cost of the flow $f$ is equal to the sum of the costs of the flows $f_i$.
My concern is not to messing up the cost of a flow with the value of a flow.
So, I want to know if is correct how I write the formula for this property:
$$f = sum_{i=1}^{k} f_i$$
graph-theory network-flow
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
$endgroup$
add a comment |
$begingroup$
I have a question about Flow Decomposition Theorem.
In the theorem say that a flow $f$ can be decompose in $k$ flows, $f_1, f_2 ... f_k$, and the cost of the flow $f$ is equal to the sum of the costs of the flows $f_i$.
My concern is not to messing up the cost of a flow with the value of a flow.
So, I want to know if is correct how I write the formula for this property:
$$f = sum_{i=1}^{k} f_i$$
graph-theory network-flow
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
$endgroup$
$begingroup$
in this script theory.stanford.edu/~trevisan/cs261/lecture11.pdf they use the notation $operatorname{cost}(f)$ for the cost of a flow (see page 3)
$endgroup$
– Pink Panther
Jan 5 at 13:30
$begingroup$
@PinkPanther and what I wrote what is suppose to mean, because I found this notation somewhere, and I don't know what wants to say. First, I think that is the cost, but now is confusing. How you can sum some flows to determine another one?
$endgroup$
– Alexander.van.Molter
Jan 5 at 13:37
$begingroup$
A flow is a function from the set $E$ of edges to $Bbb R_{ge 0}$, so we can consider a natural sum $f_1+f_2$ of flows $f_1$ and $f_2$ by putting $(f_1+f_2)(e)=f_1(e)+f_2(e)$ for each $ein E$.
$endgroup$
– Alex Ravsky
Jan 6 at 15:58
add a comment |
$begingroup$
I have a question about Flow Decomposition Theorem.
In the theorem say that a flow $f$ can be decompose in $k$ flows, $f_1, f_2 ... f_k$, and the cost of the flow $f$ is equal to the sum of the costs of the flows $f_i$.
My concern is not to messing up the cost of a flow with the value of a flow.
So, I want to know if is correct how I write the formula for this property:
$$f = sum_{i=1}^{k} f_i$$
graph-theory network-flow
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
$endgroup$
I have a question about Flow Decomposition Theorem.
In the theorem say that a flow $f$ can be decompose in $k$ flows, $f_1, f_2 ... f_k$, and the cost of the flow $f$ is equal to the sum of the costs of the flows $f_i$.
My concern is not to messing up the cost of a flow with the value of a flow.
So, I want to know if is correct how I write the formula for this property:
$$f = sum_{i=1}^{k} f_i$$
graph-theory network-flow
graph-theory network-flow
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
asked Jan 5 at 13:26
Alexander.van.MolterAlexander.van.Molter
11
11
$begingroup$
in this script theory.stanford.edu/~trevisan/cs261/lecture11.pdf they use the notation $operatorname{cost}(f)$ for the cost of a flow (see page 3)
$endgroup$
– Pink Panther
Jan 5 at 13:30
$begingroup$
@PinkPanther and what I wrote what is suppose to mean, because I found this notation somewhere, and I don't know what wants to say. First, I think that is the cost, but now is confusing. How you can sum some flows to determine another one?
$endgroup$
– Alexander.van.Molter
Jan 5 at 13:37
$begingroup$
A flow is a function from the set $E$ of edges to $Bbb R_{ge 0}$, so we can consider a natural sum $f_1+f_2$ of flows $f_1$ and $f_2$ by putting $(f_1+f_2)(e)=f_1(e)+f_2(e)$ for each $ein E$.
$endgroup$
– Alex Ravsky
Jan 6 at 15:58
add a comment |
$begingroup$
in this script theory.stanford.edu/~trevisan/cs261/lecture11.pdf they use the notation $operatorname{cost}(f)$ for the cost of a flow (see page 3)
$endgroup$
– Pink Panther
Jan 5 at 13:30
$begingroup$
@PinkPanther and what I wrote what is suppose to mean, because I found this notation somewhere, and I don't know what wants to say. First, I think that is the cost, but now is confusing. How you can sum some flows to determine another one?
$endgroup$
– Alexander.van.Molter
Jan 5 at 13:37
$begingroup$
A flow is a function from the set $E$ of edges to $Bbb R_{ge 0}$, so we can consider a natural sum $f_1+f_2$ of flows $f_1$ and $f_2$ by putting $(f_1+f_2)(e)=f_1(e)+f_2(e)$ for each $ein E$.
$endgroup$
– Alex Ravsky
Jan 6 at 15:58
$begingroup$
in this script theory.stanford.edu/~trevisan/cs261/lecture11.pdf they use the notation $operatorname{cost}(f)$ for the cost of a flow (see page 3)
$endgroup$
– Pink Panther
Jan 5 at 13:30
$begingroup$
in this script theory.stanford.edu/~trevisan/cs261/lecture11.pdf they use the notation $operatorname{cost}(f)$ for the cost of a flow (see page 3)
$endgroup$
– Pink Panther
Jan 5 at 13:30
$begingroup$
@PinkPanther and what I wrote what is suppose to mean, because I found this notation somewhere, and I don't know what wants to say. First, I think that is the cost, but now is confusing. How you can sum some flows to determine another one?
$endgroup$
– Alexander.van.Molter
Jan 5 at 13:37
$begingroup$
@PinkPanther and what I wrote what is suppose to mean, because I found this notation somewhere, and I don't know what wants to say. First, I think that is the cost, but now is confusing. How you can sum some flows to determine another one?
$endgroup$
– Alexander.van.Molter
Jan 5 at 13:37
$begingroup$
A flow is a function from the set $E$ of edges to $Bbb R_{ge 0}$, so we can consider a natural sum $f_1+f_2$ of flows $f_1$ and $f_2$ by putting $(f_1+f_2)(e)=f_1(e)+f_2(e)$ for each $ein E$.
$endgroup$
– Alex Ravsky
Jan 6 at 15:58
$begingroup$
A flow is a function from the set $E$ of edges to $Bbb R_{ge 0}$, so we can consider a natural sum $f_1+f_2$ of flows $f_1$ and $f_2$ by putting $(f_1+f_2)(e)=f_1(e)+f_2(e)$ for each $ein E$.
$endgroup$
– Alex Ravsky
Jan 6 at 15:58
add a comment |
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$begingroup$
in this script theory.stanford.edu/~trevisan/cs261/lecture11.pdf they use the notation $operatorname{cost}(f)$ for the cost of a flow (see page 3)
$endgroup$
– Pink Panther
Jan 5 at 13:30
$begingroup$
@PinkPanther and what I wrote what is suppose to mean, because I found this notation somewhere, and I don't know what wants to say. First, I think that is the cost, but now is confusing. How you can sum some flows to determine another one?
$endgroup$
– Alexander.van.Molter
Jan 5 at 13:37
$begingroup$
A flow is a function from the set $E$ of edges to $Bbb R_{ge 0}$, so we can consider a natural sum $f_1+f_2$ of flows $f_1$ and $f_2$ by putting $(f_1+f_2)(e)=f_1(e)+f_2(e)$ for each $ein E$.
$endgroup$
– Alex Ravsky
Jan 6 at 15:58