Is Binary Integer Linear Programming solvable in polynomial time?Does the independence of P = NP imply existence of arbitrarily good super-polynomial upper bound for SAT?Polynomial-time complexity and a question and a remark of SerrePartially optimal solutions in integer linear programmingIs a Parametric Integer Linear Programming Problem eventually quasi-polynomial?Under what conditions does an Integer Programming problem run in polynomial time?Feasibility Mixed integer Linear programming with quadratic constraints?Algorithm for (binary) integer programming
Is Binary Integer Linear Programming solvable in polynomial time?
Does the independence of P = NP imply existence of arbitrarily good super-polynomial upper bound for SAT?Polynomial-time complexity and a question and a remark of SerrePartially optimal solutions in integer linear programmingIs a Parametric Integer Linear Programming Problem eventually quasi-polynomial?Under what conditions does an Integer Programming problem run in polynomial time?Feasibility Mixed integer Linear programming with quadratic constraints?Algorithm for (binary) integer programming
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The paper Solving the Binary Linear Programming Model in Polynomial Time claims that Binary Integer Linear Programming is in P. However, it seems that no subsequent literature in the mainstream has done any further study on this. I am a bit doubtful regarding the correctness of the claim made in that paper.
Therefore, I have put this question here.
computational-complexity linear-programming integer-programming
asked 9 hours ago
aroycaroyc
1314 bronze badges
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add a comment |
$begingroup$
The paper Solving the Binary Linear Programming Model in Polynomial Time claims that Binary Integer Linear Programming is in P. However, it seems that no subsequent literature in the mainstream has done any further study on this. I am a bit doubtful regarding the correctness of the claim made in that paper.
Therefore, I have put this question here.
computational-complexity linear-programming integer-programming
asked 9 hours ago
aroycaroyc
1314 bronze badges
$endgroup$
add a comment |
$begingroup$
The paper Solving the Binary Linear Programming Model in Polynomial Time claims that Binary Integer Linear Programming is in P. However, it seems that no subsequent literature in the mainstream has done any further study on this. I am a bit doubtful regarding the correctness of the claim made in that paper.
Therefore, I have put this question here.
computational-complexity linear-programming integer-programming
asked 9 hours ago
aroycaroyc
1314 bronze badges
$endgroup$
The paper Solving the Binary Linear Programming Model in Polynomial Time claims that Binary Integer Linear Programming is in P. However, it seems that no subsequent literature in the mainstream has done any further study on this. I am a bit doubtful regarding the correctness of the claim made in that paper.
Therefore, I have put this question here.
computational-complexity linear-programming integer-programming
computational-complexity linear-programming integer-programming
asked 9 hours ago
aroycaroyc
1314 bronze badges
asked 9 hours ago
aroycaroyc
1314 bronze badges
asked 9 hours ago
aroycaroyc
1314 bronze badges
asked 9 hours ago
aroycaroyc
1314 bronze badges
asked 9 hours ago
aroycaroyc
1314 bronze badges
1314 bronze badges
add a comment |
add a comment |
1 Answer
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$begingroup$
Often called Binary Integer Programming (BIP).
Wikipedia:
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Here is a list of those 21 Karp problems.
You can also find the claim that BIP $in$ NPC in many class notes, e.g.,
this set.
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
$endgroup$
4
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Often called Binary Integer Programming (BIP).
Wikipedia:
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Here is a list of those 21 Karp problems.
You can also find the claim that BIP $in$ NPC in many class notes, e.g.,
this set.
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
$endgroup$
4
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
add a comment |
$begingroup$
Often called Binary Integer Programming (BIP).
Wikipedia:
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Here is a list of those 21 Karp problems.
You can also find the claim that BIP $in$ NPC in many class notes, e.g.,
this set.
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
$endgroup$
4
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
add a comment |
$begingroup$
Often called Binary Integer Programming (BIP).
Wikipedia:
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Here is a list of those 21 Karp problems.
You can also find the claim that BIP $in$ NPC in many class notes, e.g.,
this set.
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
$endgroup$
Often called Binary Integer Programming (BIP).
Wikipedia:
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Here is a list of those 21 Karp problems.
You can also find the claim that BIP $in$ NPC in many class notes, e.g.,
this set.
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
answered 8 hours ago
Joseph O'RourkeJoseph O'Rourke
88k16 gold badges248 silver badges728 bronze badges
88k16 gold badges248 silver badges728 bronze badges
4
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
add a comment |
4
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
4
4
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
$begingroup$
The cited paper actually acknowledges that BIP is NP-complete. In fact the paper explicitly claims to have proven that P = NP. That by itself is plenty reason to be "doubtful regarding the correctness of the claim" in the paper.
$endgroup$
– Timothy Chow
5 hours ago
add a comment |
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