Linear programming Set cover problem with no overlap
$begingroup$
The classical set cover problem admits overlapping (the following is the relaxed form):
$min sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) geq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
Is there a way to have no overlap of element?
I know that problem of set packing can do the job, the problem is that I want to minimize the total cost (weight) and the maximum set packing problem is the following:
$max sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) leq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
It maximize the total cost in this way and it seems not what I need.
algorithms
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
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migrated from datascience.stackexchange.com Jan 6 at 16:21
This question came from our site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field.
add a comment |
$begingroup$
The classical set cover problem admits overlapping (the following is the relaxed form):
$min sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) geq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
Is there a way to have no overlap of element?
I know that problem of set packing can do the job, the problem is that I want to minimize the total cost (weight) and the maximum set packing problem is the following:
$max sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) leq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
It maximize the total cost in this way and it seems not what I need.
algorithms
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
$endgroup$
migrated from datascience.stackexchange.com Jan 6 at 16:21
This question came from our site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field.
1
$begingroup$
It's of course possible to have no overlap if you set your constraint to = 1 and make whatever solver you are using respect it. You can read about the problem in wikipedia: en.wikipedia.org/wiki/Exact_cover . I think for these questions you'd be better of asking in other SE sites such as compsci or math.
$endgroup$
– anymous.asker
Jan 6 at 14:29
add a comment |
$begingroup$
The classical set cover problem admits overlapping (the following is the relaxed form):
$min sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) geq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
Is there a way to have no overlap of element?
I know that problem of set packing can do the job, the problem is that I want to minimize the total cost (weight) and the maximum set packing problem is the following:
$max sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) leq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
It maximize the total cost in this way and it seems not what I need.
algorithms
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
$endgroup$
The classical set cover problem admits overlapping (the following is the relaxed form):
$min sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) geq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
Is there a way to have no overlap of element?
I know that problem of set packing can do the job, the problem is that I want to minimize the total cost (weight) and the maximum set packing problem is the following:
$max sum_{S in mathcal{S}} c(S)x(S)$
s.t
$sum_{S: e in S} x(S) leq 1 forall e in U$
$x(S) in [0,1] S in mathcal{S}$
It maximize the total cost in this way and it seems not what I need.
algorithms
algorithms
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
edited Jan 9 at 18:18
CuriousMind
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
asked Jan 6 at 10:51
CuriousMindCuriousMind
32
32
migrated from datascience.stackexchange.com Jan 6 at 16:21
This question came from our site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field.
migrated from datascience.stackexchange.com Jan 6 at 16:21
This question came from our site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field.
1
$begingroup$
It's of course possible to have no overlap if you set your constraint to = 1 and make whatever solver you are using respect it. You can read about the problem in wikipedia: en.wikipedia.org/wiki/Exact_cover . I think for these questions you'd be better of asking in other SE sites such as compsci or math.
$endgroup$
– anymous.asker
Jan 6 at 14:29
add a comment |
1
$begingroup$
It's of course possible to have no overlap if you set your constraint to = 1 and make whatever solver you are using respect it. You can read about the problem in wikipedia: en.wikipedia.org/wiki/Exact_cover . I think for these questions you'd be better of asking in other SE sites such as compsci or math.
$endgroup$
– anymous.asker
Jan 6 at 14:29
1
1
$begingroup$
It's of course possible to have no overlap if you set your constraint to = 1 and make whatever solver you are using respect it. You can read about the problem in wikipedia: en.wikipedia.org/wiki/Exact_cover . I think for these questions you'd be better of asking in other SE sites such as compsci or math.
$endgroup$
– anymous.asker
Jan 6 at 14:29
$begingroup$
It's of course possible to have no overlap if you set your constraint to = 1 and make whatever solver you are using respect it. You can read about the problem in wikipedia: en.wikipedia.org/wiki/Exact_cover . I think for these questions you'd be better of asking in other SE sites such as compsci or math.
$endgroup$
– anymous.asker
Jan 6 at 14:29
add a comment |
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$begingroup$
It's of course possible to have no overlap if you set your constraint to = 1 and make whatever solver you are using respect it. You can read about the problem in wikipedia: en.wikipedia.org/wiki/Exact_cover . I think for these questions you'd be better of asking in other SE sites such as compsci or math.
$endgroup$
– anymous.asker
Jan 6 at 14:29