Maximum cover with k element
$begingroup$
I want to solve the following problem :
For two set $mathcal N$ and $mathcal E$, we have a binary matrix $A$ index by $mathcal N times mathcal E$ and we say that $ein mathcal E$ covers $n in mathcal N$ if $a_{n, e}= 1$. We are looking for the maximum set of $mathcal N$ covered by exactly $k$ elements in $mathcal E$.
I know that we can write this problem as an integer program. However, I want to have a combinatorial algorithm to solve it.
Can anyone help me to find good heuristic or an exact algorithm?
discrete-mathematics graph-theory algorithms computational-complexity
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
$endgroup$
add a comment |
$begingroup$
I want to solve the following problem :
For two set $mathcal N$ and $mathcal E$, we have a binary matrix $A$ index by $mathcal N times mathcal E$ and we say that $ein mathcal E$ covers $n in mathcal N$ if $a_{n, e}= 1$. We are looking for the maximum set of $mathcal N$ covered by exactly $k$ elements in $mathcal E$.
I know that we can write this problem as an integer program. However, I want to have a combinatorial algorithm to solve it.
Can anyone help me to find good heuristic or an exact algorithm?
discrete-mathematics graph-theory algorithms computational-complexity
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
$endgroup$
add a comment |
$begingroup$
I want to solve the following problem :
For two set $mathcal N$ and $mathcal E$, we have a binary matrix $A$ index by $mathcal N times mathcal E$ and we say that $ein mathcal E$ covers $n in mathcal N$ if $a_{n, e}= 1$. We are looking for the maximum set of $mathcal N$ covered by exactly $k$ elements in $mathcal E$.
I know that we can write this problem as an integer program. However, I want to have a combinatorial algorithm to solve it.
Can anyone help me to find good heuristic or an exact algorithm?
discrete-mathematics graph-theory algorithms computational-complexity
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
$endgroup$
I want to solve the following problem :
For two set $mathcal N$ and $mathcal E$, we have a binary matrix $A$ index by $mathcal N times mathcal E$ and we say that $ein mathcal E$ covers $n in mathcal N$ if $a_{n, e}= 1$. We are looking for the maximum set of $mathcal N$ covered by exactly $k$ elements in $mathcal E$.
I know that we can write this problem as an integer program. However, I want to have a combinatorial algorithm to solve it.
Can anyone help me to find good heuristic or an exact algorithm?
discrete-mathematics graph-theory algorithms computational-complexity
discrete-mathematics graph-theory algorithms computational-complexity
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
edited Dec 20 '18 at 17:08
Alex Ravsky
42.2k32383
42.2k32383
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
asked Dec 20 '18 at 9:22
YouemYouem
2,794419
2,794419
add a comment |
add a comment |
1 Answer
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$begingroup$
As I understood, you are asking about so-called Maximum Coverage problem. It is so well known and investigated, that I can easily provide you a very brief survey on it, containing a list of its applications, results of its computational complexity and approximability, related problems and more easy special cases. Namely, this is the beginning of the introduction of the paper “Approximation Schemes for Geometric Coverage Problems” by Steven Chaplick, Minati De, Joachim Spoerhase, and me. :-)
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
As I understood, you are asking about so-called Maximum Coverage problem. It is so well known and investigated, that I can easily provide you a very brief survey on it, containing a list of its applications, results of its computational complexity and approximability, related problems and more easy special cases. Namely, this is the beginning of the introduction of the paper “Approximation Schemes for Geometric Coverage Problems” by Steven Chaplick, Minati De, Joachim Spoerhase, and me. :-)
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
$endgroup$
add a comment |
$begingroup$
As I understood, you are asking about so-called Maximum Coverage problem. It is so well known and investigated, that I can easily provide you a very brief survey on it, containing a list of its applications, results of its computational complexity and approximability, related problems and more easy special cases. Namely, this is the beginning of the introduction of the paper “Approximation Schemes for Geometric Coverage Problems” by Steven Chaplick, Minati De, Joachim Spoerhase, and me. :-)
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
$endgroup$
add a comment |
$begingroup$
As I understood, you are asking about so-called Maximum Coverage problem. It is so well known and investigated, that I can easily provide you a very brief survey on it, containing a list of its applications, results of its computational complexity and approximability, related problems and more easy special cases. Namely, this is the beginning of the introduction of the paper “Approximation Schemes for Geometric Coverage Problems” by Steven Chaplick, Minati De, Joachim Spoerhase, and me. :-)
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
$endgroup$
As I understood, you are asking about so-called Maximum Coverage problem. It is so well known and investigated, that I can easily provide you a very brief survey on it, containing a list of its applications, results of its computational complexity and approximability, related problems and more easy special cases. Namely, this is the beginning of the introduction of the paper “Approximation Schemes for Geometric Coverage Problems” by Steven Chaplick, Minati De, Joachim Spoerhase, and me. :-)
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
edited Dec 20 '18 at 17:12
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
answered Dec 20 '18 at 17:07
Alex RavskyAlex Ravsky
42.2k32383
42.2k32383
add a comment |
add a comment |
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