All Questions
8 questions
13
votes
2
answers
664
views
Complexity of a weirdo two-dimensional sorting problem
Please forgive me if this is easy for some reason.
Suppose given $S$, a set of $n^2$ points in $\mathbb{R}^2$.
I want to choose a bijective map $f$ from $S$ to the set of lattice points in $\lbrace ...
- 19.2k
4
votes
1
answer
2k
views
Under what conditions does an Integer Programming problem run in polynomial time?
Given $AX\leq B$ where $A\in\Bbb Z^{m\times n}$,$B\in\Bbb Z^m$ finding $X\in\Bbb Z^n$ where $m\geq n$ is the integer programming problem. If $A$ is totally unimodular then the problem is solvable in ...
- 13.9k
4
votes
1
answer
204
views
Reference: Packing under translation is in NP
I am looking for a reference for a result that I am aware of.
Let me describe the result.
Given a polygon $C$ and polygons $p_1,\ldots,p_n$, it can be decided in NP
time, if $p_1,\ldots,p_n$ can be ...
- 479
3
votes
0
answers
105
views
Are there scenarios under which feasibility bilinear programming is easy?
Given $c\in\Bbb R^{n_1},d\in\Bbb R^{n_2}$, $E\in\Bbb R^{n_1\times n_2}$, $A\in\Bbb R^{m_1\times n_1}$, $B\in\Bbb R^{m_2\times n_2}$ $a\in\Bbb R^{m_1}$, $b\in\Bbb R^{m_2}$ and $t\in\Bbb R$ we know ...
- 13.9k
2
votes
1
answer
240
views
Is the problem of vertex enumeration from an H-representation of a polytope NP-hard?
According to the Wikipedia page on the issue, the vertex enumeration problem is NP-hard.
However, double description and reverse linear search are algorithms listed to solve the problem. Moreover, ...
- 123
1
vote
1
answer
206
views
Show $0-1$ Knapsack is polynomially reducible to this problem
I have already posted this question here but have not received an answer so I am cross-posting with hope to reach a larger amount of mathematicians:
Let $T=\{1,\cdots,n\}$ and consider the ...
- 225
1
vote
0
answers
1k
views
How to solve simple bilinear equations under extra linear constraints
Hello,
This is the full version of a question I asked earlier. I am trying to understand whether finding a solution to the following bilinear system is computationally hard or easy:
$\lambda_i^T u_{...
- 53
0
votes
0
answers
171
views
Solve NP-hard type problems with linear programming
I would like to know if there is any way to solve an NP-hard type problem, for example, the TSP, sum of subsets or knapsack problem, by using linear programming and not by brute force.
I ask this ...
