All Questions
Tagged with integer-programming reference-request
7 questions
6
votes
0
answers
410
views
Efficient solutions to general Bézout’s identity $a_1 b_1 + \dots + a_n b_n = 1$
Suppose I have integers $a_1, \dots, a_n$ which are coprime, meaning that
$$a_1 b_1 + \dots + a_n b_n = 1$$
has a solution in integers $b_1, \dots, b_n$.
I would like to get a bound saying ...
- 4,164
2
votes
0
answers
103
views
What does Lenstra's MILP do?
Honestly I do not understand why Lenstra's MILP is in $P$ if the number of integer dimensions is fixed.
Here is what Lenstra says in 'http://people.csail.mit.edu/rrw/presentations/Lenstra81.pdf' in ...
- 13.9k
1
vote
2
answers
753
views
basis of the lattice generated by the integer points inside a subspace of R^L
Consider $K$ linearly independent vectors $\mathbf{a}_1, \mathbf{a}_2, ..., \mathbf{a}_K \in \mathbb{Z}^L$, where $1 \leq K<L $. Hence, the span of $\lbrace\mathbf{a}_1, \mathbf{a}_2, ..., \mathbf{...
- 51
2
votes
0
answers
83
views
Reference request: Edmond's Algorithm for integer hull
I'm looking for a good reference for the algorithm (supposedly by Edmonds) to compute the integer hull of a polytope, not by cutting plane methods but by starting with a set of integer points and then ...
- 243
3
votes
1
answer
340
views
Name search for special Linear Integer Program
I am looking for a name for the following question in literature!
(and if you know it, then it would be great)
I couldn't find it and due to wide audience here, presumably you know more. Thank you
$...
- 31
1
vote
0
answers
493
views
Complexity of Nested Linear Optimization
My question is motivated by the fact, that among other ways, it is possible to restrict a variable to two discrete values, e.g. the prototypical $0$ and $1$, via an optimization constraint:
$$\max(\...
- 13.2k
2
votes
3
answers
753
views
Reference Request for Integer factorization with LP/ILP
Have there been attempts to factor integers with Linear Programming?
Searching the internet suggests that for Integer Factorization only Number Theoretic algorithms, like sieves, are taken into ...
- 13.2k