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Integer linear program for Ising ground state problem

I am trying to model the Ising spin state problem into Integer linear program and find the optimal ground state using lp_solve. (This is just a miniature version of Ising state problem) $$ maximise: ...
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1answer
13 views

Express XOR with multiple inputs in zero-one integer linear programming (ILP)

In the below post, it is explained how to express xor of two variables as linear inequalities. Express boolean logic operations in zero-one integer linear programming (ILP) Naturally, the xor of ...
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1answer
27 views

Can you generate random linear programming problems?

I looked at Linear Programming, and it are problems like this: You know that Cabinet X costs 10 cents per unit, requires 6 square feet of floor space, and holds 8 cubic feet of files. Cabinet ...
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0answers
62 views

Totally unimodular <=> polynomial time?

Crossposting due to recommendation. I formulated a MIP problem which I didn't expect to be unimodular. The problem is to find a minimum complete sequence in a strongly connected digraph. That is, ...
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2answers
52 views

Restricted Integer Programming

The integer feasibility problem is NP-complete: $Ax=b, x \geq 0, x \mbox{ integer}$ $A$ contains elements in $\mathbb{R}$ If we restrict this: $A$ contains only elements in: $\{1,0\}$ ...
3
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1answer
69 views

Find perfect matching whose weight is minimal, in polynomial time

Given a bipartite graph $G=(A,B,E)$ and a weight function $w: E \rightarrow\mathbb{R}^+$, I'd like to find a perfect matching $M\subseteq E$ with min. weight. I'm assuming $|A| \leq |B|$, and WLOG $G$ ...
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1answer
86 views

Polynominal reduction from unbounded knapsack problem to general integer programming

Given an oracle that can solve in polynominal time: $$a^Tx=b$$ $$x \geq 0$$ So it can solve the feasibility problem with one equality-constraint(a is here a vector and b is a constant, x is required ...
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1answer
60 views

Integer Programming Traveling Salesman - Checking if Tour is Complete

I'm reading a Wikipedia article on the Traveling Salesman problem as an Integer Programming formulation (http://en.wikipedia.org/wiki/Travelling_salesman_problem). The authors have all their ...
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1answer
32 views

Integer Programming - packing wolves and sheep

I'm new to linear/integer programming and I'm trying to solve a little problem I made up. I want to "pack" animals into a minimum number of bins where some of the animals cannot co-exist (wolves and ...
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1answer
37 views

Scheduling Problem Optimisation using LP solvers

I am currently working on a scheduling system which schedules individuals based on timeslot that have the following attributes : (1) Day of Week (2) Month (3) Session(AM/PM). The individuals ...
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0answers
22 views

Fastest known complexity for combinatorial ILP algorithm?

I'm wondering, what is the best known algorithm, in terms of Big-$O$ notation, to solve Integer Linear Programming? I know that the problem is $NP$-complete, so I'm not expecting anything polynomial. ...
1
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1answer
33 views

ILP and number of variables in constraints

This question is about the time impact of the length (i.e. number of variables) of the constraints in an Integer Linear Programming formulation. Most people try to reach the minimum number of ...
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26 views

How to convert a rank constraint into integer programming?

Consider the low-rank matrix completion problem: given an integer $k$ and a subset of entries of some matrix, can you fill in the rest of the entries so that the resulting matrix has rank at most $k$? ...
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2answers
36 views

What is decision version of integer programming

I dont know what is meant by decision version of Integer Programming. I know ILP, but this terminology has me confused. There are no good resources on Google.
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1answer
39 views

Integer Linear Programs: An instance or not?

Given a set of integers $\{x_0, x_1, ... , x_{n-1}, x_n\} \subseteq \mathbb{Z}$, a set of integer variables $\{y_0, y_1, ... ,y_{n-1}, y_n\} \subseteq \mathbb{Z}$ and an integer $m \in \mathbb{Z}$ is ...
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0answers
37 views

Difficulty of Integer Linear Programming vs. Mixed Integer Linear Programming

I have recently been working on an applied project where I have to solve optimization problems. I have found that it is much easier to solve an integer linear program (ILP) as opposed to a ...
2
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0answers
44 views

How can k-means be reduced to Integer Programming

The k-means algorithm reduces to computing the objective function: $ \underset{\textbf{S}}{\operatorname{argmax}} \sum_{i=1}^k \sum_{\textbf{x}_j\in\textbf{S}_i} \lVert \textbf{x}_j - \mathbf{\mu}_i ...
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73 views

Formulating Integer Program for passing packages on a cycle

Can't seem to figure out the IP formulation for this. Question Suppose there are $n$ people connected in a circular fashion as demonstrated by the diagram. Individuals need to send packages to each ...
2
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1answer
253 views

Advantage of MTZ problem formulation of TSP

In class, we saw the Miller-Tucker-Zemlin formulation of the Travelling Salesmen Problem (TSP). MTZ is a way of formulating the TSP as an integer linear programming instance. I understand how MTZ ...
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1answer
50 views

How to reformulate my problem as a mixed-integer quadratic problem

I have an unknown $n$-dimensional vector $x$ whose analytical expression depends on the following sum $x = z + Ba$ where the vector $z$ and the matrix $B\in \mathbb{R}^{n\times s}$ are given. So the ...
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0answers
92 views

Is this NP-Hard problem? [closed]

I have the following problem. maximize $\sum\limits_{k=1}^Lx_k$ subject to: $\mathbf{x}^T\mathbf{A}~ \tilde{\mathbf{x}_i} \geq 0,~~ \forall~ i\in\{1, 2, \cdots, L\}.$ where, $~\mathbf{x}^T = (x_1, ...
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2answers
244 views

Find a binary matrix so that no vector from {-1,0,1}^n is in its kernel

Given integers $n,m$, I want to find a $m \times n$ binary matrix $X$ such that there does not exist any non-zero vector $y \in \{-1,0,1\}^n$ with $Xy=0$ (all operations performed over $\mathbb{Z}$). ...
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1answer
532 views

Poly-time reduction from ILP to SAT?

So, as is known, ILP's 0-1 decision problem is NP-complete. Showing it's in NP is easy, and the original reduction was from SAT; since then, many other NP-Complete problems have been shown to have ILP ...
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0answers
788 views

Is it NP-hard to fill up bins with minimum moves?

There are $n$ bins and $m$ type of balls. The $i$th bin has labels $a_{i,j}$ for $1\leq j\leq m$, it is the expected number of balls of type $j$. You start with $b_j$ balls of type $j$. Each ball of ...
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1answer
3k views

Express boolean logic operations in zero-one integer linear programming (ILP)

I have an integer linear program (ILP) with some variables $x_i$ that are intended to represent boolean values. The $x_i$'s are constrained to be integers and to hold either 0 or 1 ($0 \le x_i \le ...
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3answers
2k views

Are all Integer Linear Programming problems NP-Hard?

As I understand, the assignment problem is in P as the Hungarian algorithm can solve it in polynomial time - O(n3). I also understand that the assignment problem is an integer linear programming ...
2
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0answers
36 views

Why are optimization problems always NP-hard and not NP-complete and what does this mean for other levels of the polynomial time hierarchy? [duplicate]

I have read that optimization problems cannot be $\mathcal{NP}$-complete, but are always classified as $\mathcal{NP}$-hard. When a problem is NP-complete, I know it is contained in $\mathcal{NP}$P. ...
8
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1answer
131 views

Hardness of Approximating 0-1 Integer Programs

Given a $0,1$ (binary) integer program of the form: $$ \begin{array}{lll} \text{min} & f(x) & \\ \text{s.t.} &A\vec{x} = \vec{b} & \quad \forall i\\ &x_i\ge 0 & \quad \forall ...