Questions tagged [mathematical-programming]
Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.
100
questions
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0answers
15 views
How to identify a continuous shape and break it into minimum number of rectangles?
The input in this case is going to be coordinates in 2D of the vertices of the shape. There will be no curves, but the shape can have holes. The algorithm or program needs to identify the continuous ...
1
vote
1answer
24 views
What easy algorithms are there for calculating products of cycle decompositions?
Here is the easy algorithm we are taught for adding two numbers in base-10 notation. We are taught this algorithm in first or second grade.
...
2
votes
1answer
38 views
Estimation of the number of solutions by Counting
This is a question from a quantum computation textbook.
Consider a classical algorithm for counting the number of solutions to a problem. The algorithm samples uniformly and independently $k$ times ...
0
votes
2answers
51 views
How many combinations will be generated if below conditions are put?
I need a generalized formula for a set having size(s) having below restrictions,
for ex. X = 2,7,11,17,26
I want only the first combination 2+7 & ignore all of the combinations that start from 2+...
-1
votes
1answer
78 views
Can we find every 216 digit number combination? [closed]
This question popped to my head when I watched Pi where the mathematican told the Jews "Didnt you calculate every 216 digit number allready?"
So I want to find every possible 216 digit number ...
0
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0answers
12 views
How to calculate constraint check in BT of 4-Queens problem?
I have seen number of constraint check in paper of CSPs.
The constraint checking is counted as followed: when a value of a variable x is checked against a value of variable y, this is counted as ...
2
votes
1answer
29 views
Linear programming IFF with equality constrain
Is it possible to write the following logical constrain in linear programming?
Let $v$ be an integer variable and $k$ an integer constant. Let $y$ be a binary variable. The logical constraint is
$y=...
0
votes
1answer
33 views
How to model equality in Integer Linear Programming
How to implement v=(a==b) using Linear Programming?
$$
v=
\begin{cases}
True, a=b\\
False, a≠b\\
\end{cases}
$$
Until now I tried the big M-Method.
To show a≤b:
$$a-b+Mv≤M$$
$$-a+b-Mv≤-1$$
To show ...
2
votes
0answers
46 views
Maximizing the product of a set of dot products
So suppose we have a set of vectors $X$ and we want to approximate the maximum of the following:
$\prod_{x \in X} b \cdot x$
where the components of $b$ sum to $1$
If it matters the components of ...
2
votes
2answers
990 views
How does a computer interpret real numbers?
I understand that the modern day digital computer works on the binary number system. I can also get, that the binary representation can be converted to rational numbers.
But I want to know how does ...
3
votes
1answer
95 views
Can this equation be solved in polynomial time?
I came across a more general form of this question.
Can we find the value of variables in polynomial time ?
Let $m = n^{2}$, there are $m$ variables ($x,y,z\ldots$) in the equation and these $m$ ...
6
votes
2answers
152 views
Can this system of polynomial equations be solved in polynomial time?
I have these $n$ equations, with $n$ variables. Variables are first $n$ positive integers, constants can be any rational number including zero. Given that there is always a solution, how do we find a ...
2
votes
1answer
24 views
Interpolate on a cylic x axes
Let's assume you are in 2D space and you have a set of fix points FIX_POINTS = [(x1, y1), (x2, y2)]. I want to interpolate the y ...
1
vote
0answers
21 views
How can I code an algorithm (concerning networks) [closed]
my question is basic but I want to know how to code algorithms containing maths like this https://web.stanford.edu/~skatti/pubs/sigcomm15-spotfi.pdf , TY for your help !
0
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0answers
26 views
Optimize an underdetermined system with quartic constraints
I encountered an optimization problem which does not belong to any well-known category of optimization.
The system has $M$ (typically $M=120$) real variables and $N$ (typically $N=100$) constraints (...
1
vote
0answers
51 views
Sum of long geometric progression [closed]
Finding sum of a geometric progression is simple when we just need to report the sum,
but when some modulo or multiplicative inverse is asked of that sum the task become tedious for me.
I have a ...
0
votes
0answers
36 views
How to generate evenly distributed random numbers from the tics of a Geiger Counter?
How can I generate random numbers from the tics of a Geiger Counter?
Say I have a file with the timestamps for every event.
0
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456
920
....
The time spans ...
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0answers
33 views
How much of the x86 instruction set does blender use? [closed]
I'm trying to better understand benchmarks that are commonly used for computer hardware. I've been unable to find an answer to this question. Extra credit if you can provide a breakdown in ...
0
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0answers
26 views
Algorithm for placing objects inside a square from outside to inside
I have a map that is 300x300 units. I have to place squares of 20x20 units inside that map from outside to inside. There are 3 different types of square, the space available inside the map needs to be ...
0
votes
1answer
49 views
Counting the number of multiples of number A that perfectly divides the number B
What is the best way of counting the number of multiples of number A that perfectly divides the number B.
This is the sub problem for one of the questions I am solving on codechef.
This is the best I ...
2
votes
1answer
89 views
Mathematically calculating time complexity
This is a thread about mathematically calculating time complexity of nonlinear functions. I know that those questions were asked a lot, but it didn't make me understand fully the subject.
Also I ...
4
votes
0answers
101 views
Count number of pairs $(a,b)$ in an array such that $(a + b)$ divides $(a * b)$
We are given an array of size $N$ with integer entries $> 0$. We have to count the number of all such pairs $(a,b)$ with $a \leq b$ such that $a*b$ is divisible by $a + b$.
The obvious naive way ...
0
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1answer
58 views
0
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0answers
71 views
What is the time complexity of MATLAB's ode solvers?
Say I have a system that is $n$ differential equations that are all coupled together, over a time interval $[a,b]$ with timestep $t$. Is there a straightforward time complexity for MATLAB's built in ...
2
votes
1answer
46 views
Implementing Gauss–Legendre algorithm using arbitrary-length rationals
I am trying to re-implement SuperPI myself in Rust, but the results I get are not very accurate. SuperPI computes pi using the Gauss-Legendre algorithm.
The Gauss–Legendre algorithm is quite simple, ...
1
vote
1answer
24 views
What is the equation for a spiral path in 3D? [closed]
I am developing games in Unity 3D. Currently, I am trying to place 3D objects in 3D space in a spiral pattern that looks like one of 2 the strands in a pair of the DNA (helix) spiral pattern.
Would ...
0
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0answers
26 views
Classify manifolds with neural networks
Can a neural network be used to find the genus of a 2-manifold given for instance as a CW complex?
1
vote
1answer
58 views
Balance groups based on average, element constraints and size
It's a complex situation, where I want to balance groups of numbers based on the average of these numbers, while keeping the group size unchanged and not breaking elements constraints.
Let me explain ...
2
votes
2answers
185 views
Implications of Integral linear program
Let $(P)$ an Integer Linear Program, where we aim to find $x\in \{0,1\}^n$ maximizing a linear function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ under some linear constraints $Ax\le b$
Let $(P^*)$ be ...
1
vote
1answer
416 views
Efficient streaming sort
Consider following task: we have an input of N+1 lines, where first line contains N - number of items, and then we have N lines, each one contains one item, which is a tuple (number id, number m), id &...
2
votes
1answer
53 views
Is there way to calculate $\sum_{i<j<k\leq n} A_i \cdot A_j \cdot A_k$ faster than $O(n^3)$
Given array $A$ of size $n$, we want to calculate $\sum_{i<j<k\leq n} A_i \cdot A_j \cdot A_k$. Is there way to speed this up rather than the standard $O(n^3) $ calculation with 3 for loops. I ...
1
vote
1answer
17 views
PCA with Bishop's book
I am reading PCA in Bishop's Pattern Recognition and Machine Learning pg. 562, here in Lagrange multiplier but I don't get it in the highlighted: I wonder is it $u_1$ or $u^T_1$?
Your help is ...
0
votes
1answer
62 views
Compute e^x given starting approximation
I have been looking for an algorithm to calculate $e^x$ to arbitrary precision (millions of digits). The best way I know is to use Taylor polynomials. However, the Taylor polynomial algorithm seems ...
1
vote
1answer
22 views
Sum of distances between points on one-dimensional axis
We have given integer array of $n$ points, let it be $A$, showing where it is on the x-axis. For this problem we are working only with the x-axis and the y-axis is not important at all. Now for given ...
3
votes
3answers
165 views
Is it possible to make a language that can build upon itself perfectly?
First of all, note that I'll have to explain my thoughts in a layman's terms.
There are so many high-level programming languages out there that compete with each other. This means we have to build ...
0
votes
2answers
817 views
Is global non-convex optimization NP-complete?
Assume I have some non-convex function $f(x_1, x_2, ...)$ and I want to optimize it to find a global minimum. I feel like it is easy to show that this problem is in the class NP with the decision ...
1
vote
1answer
37 views
How do you implement a language with greater capabilities using subordinate languages?
I've heard that C++ and Python where implemented using C. How can someone make an object oriented language out of something that doesn't support objects?
I've read in the book "Math You Can`t Use - ...
1
vote
1answer
153 views
Algorithm for weighted elliptic curve fit
Background:
I was trying to detect a face solely on the bases of features and the confidence of the features found.
I am using a method to identify the features along with the response (confidence). ...
0
votes
1answer
153 views
Is there a poly-time algorithm for expanding out polynomials
so I've been looking around and haven't seen this before. Basically I'm working with a problem in which I need to expand/FOIL out. Something in the form of
$$
z = (x+y)(x-y) \implies x^2+xy-xy+y^2
$$
...
1
vote
1answer
87 views
Is it possible to evaluate $n!$ in $O(1)$?
I'm working on a formula that'll evaluate the partial sum of the harmonic series from $t_1$ to $t_n$. The problem is that I'm almost certain the final formula will include factorials. But if the ...
1
vote
2answers
281 views
Algorithm for packing various shapes inside of a rectangle
Say I am given a rectangle of width $W$ and length $L$. I now have to fit as many regular shapes of area $A$ into this rectangle as possible. For example, if the shape is a circle, I need to fit as ...
4
votes
2answers
252 views
Is the $x$ in $\frac{\mathrm{d}}{\mathrm{d}x}$ a symbol in the sense of Harper's PFPL?
The role of $x$ in $\frac{\mathrm{d}}{\mathrm{d}x} y$ not only confuses my calculus students, it has also puzzled some well known mathematicians. Questions one might ask are:
Does the $x$ in the ...
0
votes
0answers
52 views
Math behind path tracing
I seem to remember seeing somewhere (many years ago) a writeup of the math behind calculating the outline of Metafont glyphs. The basic idea is you have a "pen" that is a circle or oval, that you ...
1
vote
1answer
109 views
What are some of the practical applications of functions that extract the exponent and mantissa of a floating point number?
I'm talking about functions such as Python's math.frexp() :
math.frexp(x)
Return the mantissa and exponent of x as the pair (m, e). m is a float
and e is an integer such that x == m * 2**e ...
0
votes
0answers
379 views
Derivatives involved in Bilinear interpolation
If we choose a unit square in which the four points where the function $f$ is known are as shown in the diagram the interpolation formula for $f$ is:
\begin{equation}
\begin{split}
f(x+u, y+v)\approx (...
1
vote
1answer
65 views
Algorithm which finds the maxmal solution that satisfies the following constraints
I have $a_1, a_2,\dots,a_n$ and $b_1,b_2,\dots,b_n$ and an upper bound $U$ and $n$ linear equations of the form:
$k_1 * a_1 + b_1 = x$
$k_2 * a_2 + b_2 = x$
$\dots$
$k_n * a_n + b_n = x$
...
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0answers
54 views
How to model the constraint of a circle placement problem mathematically?
I have a circle with radius $R$ and $N$ points on a 2D plane with known locations $(x_i,y_i), i=1,2,..N$. I want to place the circle such that it maximizes the number of covered points.
Let $d_i=(x_i-...
0
votes
1answer
61 views
How can I calculate the new quotient if I came to know divisor is increased by one?
If I have two number consider a and b and let their division quotient is c.
I know the value of c but I don't know either value of divided(a) or divisor(b). If I came to know the value of divisor is ...
2
votes
1answer
137 views
How to find the most unique vectors in a set?
A question bridging math and computer science, I have on the order of 10000 vectors each of a equal but high dimension, say 6 or 7 dimensions. I want to find a given number of 'unique' vectors in the ...
2
votes
0answers
122 views
Can cognitive architectures (CLARION, SOAR, ACT-R) be used for creative mathematical reasoning?
Can cognitive architectures (CLARION, SOAR, ACT-R, others) be used for creative mathematical reasoning? As far as I understand, then it is the best to encode formal mathematical knowledge in the ...
