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# Questions tagged [integer-programming]

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### The set of weight functions for which the assignment problem has non-trivial solutions

The standard assignment problem is specified with a square matrix ${\bf W}$ of weights (values, costs): $$V_{\cal P} = \sum_i w(i, b(i)) = \sum_{(i, j) \in {\cal P}} w_{ij},$$ where $\cal P$ is a ...
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### What is the complexity of Parametric Mixed Integer Linear Programming?

We know $$\forall\bf y\in\mathbb Z^n:K\bf y\leq b$$ $$\exists\bf x\in\mathbb Z^m:A\bf x + B\bf y\leq c$$ is in $\bf P$ if $n,m$ are fixed from Kannan's result (refer page $1$ in reference). What is ...
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### Polynomial cases of 0 1 quadratic programm with linear constraints

A pseudo boolean function f:{0,1}^n-> R is defined as f(x)= x^tQx +cx where Q is a symmetric matrix with null elements in the diagonal. Finding the minimum of this function is solvable in polynomial ...
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### Fixed parameter Integer Programming circuit depth complexity

It is well known Lenstra's and Kannan's algorithm achieves $n$-variable parameter $L$-bit integer programming solvability in $O(n^nL)$ time and $O(L)$ space. If implemented as an arithmetic circuit ...
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### 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 ...
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### Interpolating the Tutte polynomial at the values of two hyperbolas

In a MO question basically I asked when the Tutte polynomial of planar graph can be uniquely determined by the polynomially computable values at the special points and at the two hyperbolas. The ...
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### Linear ordering of bipartite tournament graphs

I have an ordered bipartite graph such that every node of the first node set is connected to every node in the second node set by an edge of a given direction (i.e., a so-called bipartite tournament ...
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Consider the following set. $S_n =\{ (x,y) ~|~x \in \mathbb{Z}_+~\wedge~ y \in \{0,1\}^n ~\wedge~x=\sum_{i=0}^{n-1} 2^i y_i \}$ $S_n$ is a collection of pairs $(x,y)$, where $x$ is an integer ...
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### Small number of inequalities defining integer hull of integer programming problem

In integer programming problem, we often want to relax the integer programming problem to linear programming problem. So we want to find the integer hull of the problem. The number of inequalities to ...
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### Paper about the upper bound of the number of inequalities to describe the Integer hull of a polyhedron

I am interested in the upper bound of the number of inequalities to describe the integer hull of a polyhedron. That is, given an integer programming problem with n inequalities which construct a ...
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### Lattice-based algorithms in practice

Are there any applications of lattice-based algorithms other than those in cryptography and integer programming? Could someone state a few papers where the primary algorithms use lattice-based LLL ...
Are there known algorithms for the following problem that beat the naive algorithm? Input: matrix $A$ and vectors $b,c$, where all entries of $A,b,c$ are nonnegative integers. Output: an ...