Questions tagged [mathematical-programming]

Using a computer to implement mathematics. For questions about (mathematical) optimization, (also) use the optimization tag.

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475 views

Given a set of points in the plane all laying on the axis, find the number of right angled triangles

My approach:- I separated the x coordinates and y coordinates in 2 separate arrays..then i used the idea of pythagoras theorem by selecting three vertices(1 from x axis and 2 from yaxis and vice versa)...
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2answers
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Being stuck and frustrated with my masters project

I'm doing a masters in CS that requires me to implement from scratch most of the neural network models and because python libraries aren't applicable to what i want. The problem is that i don't feel ...
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Automatically detect Object points and Image points from a Single Grid for Camera Calibration?

What is the best generalised algorithm suited for detecting Object points and image points automatically from a single grid image with different line thickness and luminance intensity? Link defining ...
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Counting triplets from three arrays satisfying the equation x^2 = yz

Let's say I have three arrays of positive integers X, Y and Z. You can assume that each of ...
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51 views

Algorithm Analysis - Binary Search Algorithm

The problem is from Data Structures and Algorithm Analysis Edition 3.2 (Java Version) Book from Clifford A. Shaffer. It is from the third chapter exercises, problem number 3.13.20. Below is how it is ...
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1answer
42 views

Why do we need/use operator precedence for Arithmetic operators?

Why do we use operator precedence rule for Arithmatic operators? Can't we simply just do the operation in a linear manner from left to right or vice-versa and deal with the operator that comes first. ...
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Proof of Fundamental Lower Bound on Regret

Online Convex Optimization sees optimization as a continuous process in which the algorithm learns new aspects of the problem and improves upon. Every iteration consists of the player making a ...
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1answer
67 views

Min-plus matrix multiplication implementation

I had a look at topological sorting where they mention a possible parallel algorithm that relies on matrix multiplication, but using min-plus matrix multiplication: One method for doing this is to ...
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2answers
107 views

Fermat's last theorem: How to (partially) solve by programs

No three distinct positive integers $a, b, c$ can satisfy the equation : $a^n + b^n=c^n$, if $n$ is an integer greater than two. The above statement, known as the Fermat's last theorem is proven ...
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Numerical integration of a function

For a particular physical system, the force is given by $$F(r)=-\frac{d\Phi(r)}{dr}=\frac{r^5+2ar^3+a^2r-4a}{r^4(r^3+ar+2a)}$$ where $\Phi(r)$ is the potential energy which can be obtained as the ...
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2answers
114 views

Find lines segment portions close together

I have two lines segment in 3D space. Lines segment are defined by 2 points each: $A_1$, $B_1$ and $A_2$, $B_2$ (see left part in the below schema). I would a like to find an algorithm to detect ...
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Are regular languages and their regular expressions part of computer science?

I am trying to understand if regular languages and their regular expressions are concepts of computer science in general and if these are discovered, or invented, by computer scientists, in particular....
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Do all the numbers belong to same slot in the Hashtable?

I was reading the CLRS. In the Hashing Chapter on page 262 a statement says: "For example, if we know that the keys are random real numbers $k$ independently and uniformly distributed in the range $0 \...
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Number of multiplications and additions in the given code

$N:=2^p$ Input: $f \in \mathbb C^N$ 1: $n=N/2$ 2: initialize vectors $f^{(1)}, f^{(2)} \in \mathbb C^n$ 3: $w_N^0=1$ 4: for $j=0,\ldots,n-1$ do 5: $\ \ \ \ \ f_j^{(1)}=f_j+f_{j+n}$ 6: $\ \ \ \ ...
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How can I calculate the exponential integral?

(I'm not sure this is the right forum.) I'm writing a program that uses the prime-counting function. Right now, I'm using x/log(x), but I want to switch to ...
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2answers
52 views

Dividing 2 integers with some constraints

This a problem i came across while practicing binary search. Here is the problem: Given two integers dividend and divisor, divide two integers without using multiplication, division and mod operator. ...
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Calculating the maxima of a function subject to a constraint

The first figure below shows the plots of a function $f(x)$ plotted for different values of a parameter $\lambda$, i.e., $f(x)=f(x,\lambda=\lambda_i);i=1,2,3,..;\lambda$ is maximum for the topmost ...
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1answer
68 views

Computer Vision Techniques to find Slope of beach in the 2D Images?

What I am planning to do is to calculate the height and estimate the slope of the segmented Object. The camera will be static and the Object of Interest is the slope of the beach. I am finding harder ...
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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 ...
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1answer
26 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. ...
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1answer
42 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 ...
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2answers
55 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+...
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1answer
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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 ...
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Need some help implementing backjumping algorithm

I am extending aima csp solver in my project.I have read the AIMA book and the book says Backjumping algorithm can be implemented by with a little modification of Backtracking algorithm.But,I don't ...
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1answer
35 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=...
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1answer
63 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 ...
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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 ...
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2answers
1k 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 ...
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1answer
109 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 $m$ ...
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157 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 ...
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1answer
34 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 ...
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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 !
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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 (...
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54 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 ...
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0answers
38 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 ...
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28 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 ...
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1answer
50 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 ...
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1answer
120 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 ...
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108 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 ...
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86 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 ...
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1answer
54 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, ...
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1answer
33 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 ...
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27 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?
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75 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 ...
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2answers
231 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 ...
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1answer
811 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 &...
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1answer
55 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 ...
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1answer
19 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 ...
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1answer
74 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 ...