Questions tagged [integer-programming]
Integer programming regards optimization problems, where one seeks to find integer values for a set of unknowns, that optimizes the objective function. A common subset of this type of problems are integer linear programming problems, where all inequalities, equalities and the objective function are linear in the unknowns.
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Reliability of ILP approach to number-theoretic optimization
This question is inspired by the recent answer, where @RobPratt proposed to use integer linear programming (ILP) for solving a number-theoretic optimization problem. I will consider a very similar ...
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Only trivial solution to a pair of constrained linear diophantine equations
Given positive integer $n$, we are looking for a set
of $n$ positive integers $a_i$.
The following linear integer program must have only
the trivial integer solution of all ones.
$0 \le x_i \le \frac{...
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What is the probability of interpolating the Tutte polynomial of a planar graph from the values at the two hyperbolas?
The Tutte polynomial
is a bivariate polynomial with positive integer coefficient which is a graph
invariant and can be defined recursively.
Evaluating it is $\#P$-complete even when restricted to (...
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votes
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Maximize the determinant of Boolean combinations of positive definite matrices
I have the following optimization problem.
$$\begin{array}{ll} \text{maximize} & \det \left(\sum^n_{i=1}z_i W_i \right)\\ \text{subject to} & \sum_{i=1}^n z_i = N\\ & z_i
\in \{0,1\}\end{...
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What are the definable sets in Skolem arithmetic?
Definable subsets of $\mathbb N$ in the language of Presburger arithmetic are exactly the eventually periodic sets and quantifier free part corresponds to Integer Programming with linear inequalities ...
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Simplified knapsack problem
There is a problem that I can not solve.
Given a set of items (each item has some integer weight) we have to fill bag with some number of copies of these items, with the only restriction that the ...
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Sufficient condition for solvability of linear diophantine system
I would like to know under what conditions does an integer solution exist to the under-determined linear system:
Ax = b. (without constraints)
Where A is m x n matrix with positive integers entries (...
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Minimal solution of simultaneous congruences
I would to determine the set of values $\lbrace a_1,a_2,a_3,\ldots,a_n \rbrace$ that minimizes the value of $x$ such that:
$$x\equiv a_1\mod p_1$$
$$\vdots$$
$$x\equiv a_n\mod p_n$$
where every ...
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