Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [integer-programming]

Questions on optimization constrained to integer variables.

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.

Integer programming is NP-hard. A special case, 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.

Source: https://en.wikipedia.org/wiki/Integer_programming

966 questions
87
votes
2 answers

Determining information in minimum trials (combinatorics problem)

A student has to pass a exam, with $k2^{k-1}$ questions to be answered by yes or no, on a subject he knows nothing about. The student is allowed to pass mock exams who have the same questions as the real exam. After each mock exam the teacher tells…
Sergio
  • 3,270
  • 12
  • 24
17
votes
5 answers

Good software for linear/integer programming

I never did any linear/integer programming so I am wondering the following two things What are some efficient free linear programming solvers? What are some efficient commercial linear programming solvers? It would be nice to supply a dummy…
Jernej
  • 4,827
  • 1
  • 29
  • 49
16
votes
3 answers

How close are the closests cells of the same color in a periodically colored grid?

In a square grid, if we have a coloring of the form $c(x, y) = (x + ny) \bmod m$, what is the minimum (positive!) taxicab distance (i.e. sum of absolute value fo coordinates) between different cells of the same color? (In this example I colored…
Herman Tulleken
  • 3,326
  • 17
  • 34
11
votes
0 answers

Balanced linear partitioning of a set of points in $R^d$

Suppose we have a set of points in $R^d$ and for a given constant $\epsilon>0$ we want to find a hyperplane such that it divides the dataset into two balanced partitions, and that the number of points that are $\epsilon$-close the hyperplane is…
kvphxga
  • 533
  • 3
  • 15
9
votes
2 answers

How to find LCM of two numbers when one starts with an offset

In the world of natural numbers, a RED and a GREEN guy start from 0 and walk down the numberline. If the RED guy moves in steps of size r and the GREEN guy moves in steps of size g, the spots on the numberline where both will step are k * lcm(r, g)…
raghavsood33
  • 251
  • 3
  • 6
8
votes
1 answer

Integer programming feasibility is NP-what

What is the complexity class of the general problem of integer programming feasibility? The sources I've looked at are, in my opinion, very confusing. Some say NP-hard, some say NP-complete. Some do not distinguish between the general problem and…
Eric Stucky
  • 12,422
  • 3
  • 32
  • 66
8
votes
3 answers

How to formulate Unique value constraint in Integer Programming?

Given the following integer programming formulation, how can I specify that the variables are unique and none of them has the same value as the other one. basically x1, x2, x3 , and x4 need to get only one unique value from 1, 2, 3 or 4. and same…
Is7aq
  • 183
  • 1
  • 4
8
votes
4 answers

Are there ways to solve equations with multiple variables?

I am not at a high level in math, so I have a simple question a simple Google search cannot answer, and the other Stack Exchange questions does not either. I thought about this question after reading a creative math book. Here is the question I was…
Mr. Star
  • 105
  • 5
7
votes
1 answer

XORing consecutive integers has an interesting property. Does anyone know why?

I hesitated to post on StackOverflow but I think the problem has little to do with programming and more to do with mathematics. So, here it is: I wanted to compute the function $ f(n) = 0 \oplus 1 \oplus 2 \oplus \dotsb \oplus n$ in O(1) instead of…
Cranium
  • 173
  • 5
7
votes
3 answers

Integer Programming problem

I have an integer programming problem with $L$ variables $x_1, x_2, x_{L}$ which all assume integer values and the following constraints must stand: $x_i \geq 0$ $x_1 = 10$ $x_2 + x_3 + ... + x_{L} = 36$ how can I find the max and min of the…
Matteo
  • 167
  • 13
7
votes
2 answers

Best approximation of sum of unit vectors by a smaller subset

Let $v_1,\ldots,v_N$ be linear independent unit vectors in $\mathbb{R}^N$ and denote their scaled sum by $s_N = \frac{1}{N}\sum_{k=1}^N v_k.$ I would like to find a small subset of size $n$ among those vectors such that their scaled sum approximates…
g g
  • 2,399
  • 8
  • 23
7
votes
2 answers

Mean and Median in a Classic River Crossing Problem

Consider the following classic problem: Four people on the west side of a river wish to use their single boat to get to the east side of a river. Each boat ride can hold at most two people, and the time it takes to get across will be the time…
Benjamin Dickman
  • 13,259
  • 2
  • 39
  • 82
7
votes
1 answer

Integer linear programming constraint for maximum number of consecutive ones in a binary sequence

Consider an integer programming problem with binary decision variables $x_1,\ldots,x_n \in \{0,1\}$. Im trying to model the constraint that enforces the maximum number of consecutive ones in successive sequence. That is, if the maximum number of…
ELEC
  • 1,103
  • 1
  • 8
  • 24
7
votes
2 answers

How to prove that this matrix is total unimodular

This matrix is total unimodular (tested by a computer program). 1 1 1 1 -1 -1 -1 -1 0 1 1 1 0 -1 -1 -1 0 0 1 1 0 0 -1 -1 0 0 0 1 0 0 0 -1 1 0 0 0 -1 0 0 0 1 1 0 0 -1 -1 0 0 1 1 1 0 -1 -1 -1 0 1 1 1 1 -1 -1 -1 -1 Is there way to prove…
JohnCry
  • 71
  • 2
6
votes
1 answer

Are packing (i.e., independence) numbers arbitrarily smaller than fractional packing (i.e., Rosenfeld) numbers?

Take a graph $G=(V,E)$. One of the equivalent ways of defining its independence number (also known as $1$-packing number) is $$\alpha = \max\left\{ \sum_{v\in V}f(v) : \forall v\in V, f(v) \in \{0,1\}\text{ and } \forall \text{ clique }C, \sum_{v\in…
user332582
  • 352
  • 1
  • 10
1
2 3
…
64 65