Questions tagged [algorithms]

A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.

6
votes
2answers
7k views

The easiest way to find intersection of two intervals

Right now I stuck with a problem. It seems to be really trivial one, but still it is hard for me to find an appropriate solution. The problem is: One has two intervals and are to find the intersection ...
4
votes
1answer
348 views

Fast algorithm for computing matrix square root using randomized linear algebra?

Is there a fast algorithm for computing the matrix square root of a real symmetric matrix using random matrices or randomized algorithms?
5
votes
4answers
2k views

Simulated Annealing proof of convergence

I implemented downhill simplex simulated annealing algorithm. Algorithm is very hard to tune, w.r.t. parameters including cooling schedule, starting temperature... My first question is about ...
2
votes
1answer
127 views

What is the name of the optimization algorithm that uses random sampling?

I am generating random weight as per e.g. below. The I generate a set of 3 values say 100, 250, 300 and I multiple them with the weights below Initial population. ...
0
votes
1answer
388 views

Drunken Man in Matlab

I wrote a script that plots the results of the "drunken lamppost" problem in MATLAB. Now I need to create a road-width from -3 to +3, length from 0 to infinity but the drunk can walk just ahead. It ...
19
votes
4answers
3k views

Is Fortuna or Mersenne Twister preferable as an algorithmic RNG?

A recent answer mentioned the use of Fortuna or Mersenne Twister Random Number Generators (RNGs) to seed a Monte Carlo simulation. I hadn't heard of Fortuna before so I looked it up - looks like it is ...
7
votes
2answers
694 views

Bin-packing: Maximise number of bins / “Fukubukuro” problem?

I recently encountered a problem that looks like a variation of bin packing or knapsack problem, but with the objective to maximise the number of bins/knapsacks: Consider there is a list of M items ...
7
votes
4answers
247 views

Testing for stability of a simulated dynamical system

Background and question I often work with simulations of dynamical systems and I usually track a single parameter $x$, such as the number of agents (for agents based models) or the error rate (for ...
1
vote
3answers
235 views

Traveling Salesman Problem

First off some context. The Traveling Salesman Problem(TSP) is to find the most efficient route passing through a series of points only once. However, there is no perfect function to solve for this in ...
0
votes
1answer
55 views

Chip testing problem

An engineer has n supposedly identical integrated-circuit chips that in principle are capable of testing each other. The engineer test jig accommodates two chips at a time. When the jig is loaded, ...
1
vote
1answer
54 views

How to find a pair of divisors as close as possible to each other?

For a given integer $n\in\mathbb{N}^*$, I want to find a pair $(x,y)\in{\mathbb{N}^*}^2$ such that $x*y=n$ and $|y-x|$ is as small as possible. A naive algorithm I found is : ...
0
votes
1answer
110 views

Finding a shortest path in a graph

If each edge of a graph $G$ is unweighted or has equal weights, then the shortest path between two nodes in that graph is the path that contains the fewest number of edges. Such a path can be obtained ...
-1
votes
0answers
41 views

What kind of standard deviation must be used in optimization algorithms?

I would like to ask about the standard deviation of objective function value. There are two types of standard deviations ° Population standard deviation ° Sample standard deviation In ...
1
vote
0answers
74 views

Find a vector B that minimizes |W-A*B|

I want to find a candidate vector $B$ that $$\min|(W - A_i * B_i)|$$ $$ a_i > 0,\ A_i=\{a_0,...,a_i\},\ B_i=\{-1,0,1\}^i$$ For example, given $$W = 0.6,\quad A_4 = [0.1, 0.2, 0.4, 0.7] $$ one ...
4
votes
1answer
36 views

Single-variable multimodal derivative-free optimization (for a well-behaved function)

Are there well-established approaches to single-variable multimodal optimization? Given $f:\mathbb{R}\rightarrow\mathbb{R}$ that: has several local minima within a given range of interest $[a,b]$ is ...
2
votes
1answer
65 views

How to justify using available code (in different language) for comparing algorithms

I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm from the literature. Our algorithm is in MATLAB, ...
1
vote
3answers
106 views

Clustering with points lying along different 3D planes

I have a bunch of data points in 3D that lie along a few planes. What would be the best approaches to estimate the normals of these planes? Edit: There are roughly equal number of points lying along ...
7
votes
1answer
139 views

Element-wise thresholding a low-rank matrix in O(n) time?

Define the element-wise thresholding operator $T_\tau(\cdot)$ with threshold $\tau$ as $$ [T_\tau(X)]_{i,j} = \begin{cases} X_{i,j} &\mbox{if } |X_{i,j}| \ge \tau, \\ 0 & \mbox{if } |X_{i,j}|...
0
votes
1answer
66 views

Stability of PDEs

I am currently trying to solve some PDEs with FiPy. At page 56, the manual mentions (https://www.ctcms.nist.gov/fipy/download/fipy-3.0.pdf). The largest stable timestep that can be taken for this ...
2
votes
0answers
45 views

Cover a polygon with least amount of parallelograms [closed]

I am solving the task that is as follows: Input: a polygon. Can be any kind of polygon without self intersections. Can be a non-convex and with holes inside. Goal: to cover it with 2 (at least) or ...
1
vote
0answers
33 views

How to numerically calculate the transition dipole integral in periodic systems?

Now I have wave functions $\psi_a$ and $\psi_b$ of two states in Gaussian CUBE format. I'd like to evaluate the transition dipole moment integral $\pmb\mu$ between these two states. As my simulation ...
0
votes
1answer
70 views

Python sequence cluster exercise

I am working through an exercise in my textbook and implementing the code in Python to practice dynamic programming. I feel like I am right on the edge of figuring it out, but after many hours, I come ...
1
vote
0answers
35 views

Number of $S_n$-orbits in $P^k(\{1,\dots,n\})$

This is a particular case of a question I asked on Mathematics Stackexchange, question which got no answer so far. Let $n$ and $k$ be integers with $n\ge1$, $k\ge0$, and let $a(n,k)$ be the number of ...
1
vote
0answers
16 views

Piecewise-linear Continuations vs Marching Squares/Cubes

It seems that both piecewise-linear continuation and marching squares are methods to produce iso-contours of a scalar function given the function's values on a grid. It seems that piecwise-linear ...
6
votes
1answer
230 views

Eigenvector with maximum overlap

Given a matrix $M$ and a vector $v$, is there an efficient method to find the normalized eigenvector of $M$ that is closest to $v$, in that it has maximal overlap. More explicitly, a vector $v$ can be ...
3
votes
1answer
56 views

Radiation heat transfer between surfaces

I'm trying to model the temperature distribution over a curved surface. Apart from the heat equation, I need to take into account the energy emission/absorption through electromagnetic radiation. The ...
0
votes
0answers
14 views

Finding Duplicate Pixel/Objects along Image seams

I have a seam of two images joined by merging algorithm that on occasion generates duplicated pixels/objects/artifacts on both sides of the seam. The images are large and currently the seams are ...
0
votes
3answers
291 views

Full segmentation of a linear space using a clustering algorithm

Once again, I am not entirely sure how to describe what I am looking for, hence I have a hard time finding answers using Google or any other literal search method. Let's say I have a time series: $$(...
7
votes
6answers
6k views

Python implementations of Gillespie's direct method

I'm looking for a decent implementation of Gillespie's Direct Method in Python, as if I code the algorithm myself I'm nigh positive I'll do it inefficiently. Anyone have a favorite?
0
votes
1answer
19 views

Binary tree for 2 elements [closed]

I want to understand Binary Search for 2 element list made of 1,2. I draw a tree as below. Is it correct? If I want to search for an element 2, it will make 2 comparisons. If I want to search for ...
2
votes
0answers
214 views

Discrete-time Algebraic Riccati Equation (DARE) solver in C++

I need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation of it ...
7
votes
2answers
2k views

Markov (Chain) image generators?

Markov Chains can be used to generate, or auto-complete, text. https://en.wikipedia.org/wiki/Markov_chain#Markov_text_generators Training text is read, and some information about the text is ...
2
votes
0answers
57 views

Where does the seemingly official number of certain algorithms come from?

There are a lot of algorithms which seem to have been supplied an official number, such as Algorithm 76, Hierarchical clustering using the minimum spanning tree. Another example is Algorithm 123, ...
0
votes
1answer
60 views

tea bag flavors mixing algorithm [closed]

I bought three boxes of tea bags with different flavors (A, B, C). I wish to mix them in such a way that - there is never two consecutive bags of the same flavor (ABCCAB is avoided) ; - the mixing ...
3
votes
0answers
92 views

FFT-based Image Rotation Algorithms More Accurate Than Chirp-Z?

We're currently using a Chirp-Z based implementation: R. W. Cox and R. Tong, "Two- and three-dimensional image rotation using the FFT," IEEE Trans. Image Processing, vol. 8, no. 9, pp. 1297–1299, Sep....
6
votes
1answer
361 views

Matching/Assignment Problem

I'm not sure how I can represent and solve the following problem. I have a list of sales (timestamp and quantity) and a list of corresponding inventory draws (timestamp and quantity). What I ...
4
votes
5answers
9k views

How to solve block tridiagonal matrix using Thomas algorithm

Thomas algorithm can be used to solve a tridiagonal matrix: $$ \begin{bmatrix} {b_ 1} & {c_ 1} & { } & { } & { 0 } \\ {a_ 2} & {b_ 2} & {c_ 2} & { } & { }...
2
votes
1answer
91 views

Accurate and efficient computation of the inverse Langevin function

The Langevin function $\mathcal{L}(x) = \mathrm{coth}(x) - \frac{1}{x}$ occurs in computations related to elastomers and paramagnetic materials. It is easily computed accurately and with high ...
1
vote
1answer
72 views

Pivoting in Block LU

What are common methods to choose pivot blocks in Block LU (for non-SPD/non-Diagonally Dominant Matrices)?
2
votes
0answers
72 views

Kernel independent fast multipole method for Yukawa potential [closed]

Has anybody used the KIFMM (https://web.stanford.edu/~lexing/fmm.pdf) for the Yukawa potential?
1
vote
2answers
75 views

Ranking Sewer Lines worst to best condition using Genetic Algorithm?

Problem I work for a municipality and we are trying to figure out which sections of sewer lines to replace first or at least identify areas that should be looked at. It was suggested I use a Fast ...
1
vote
0answers
169 views

Use of Morton Key to reduce number of grid points

I asked a question on Stack Overflow Performance Issue with VP Trees and Nearest Neighborsand I was not satisfied with the answer and so I thought I would reword my question for this site and post ...
3
votes
0answers
72 views

First order methods for a large scale semidefinite program

I am interested in solving the following semidefinite optimization problem: \begin{equation} \begin{split} \underset{X,\lambda}{\rm maximize} \;\;\;\;&\lambda^Tc \\ &-\mathbb{I} \le X \le \...
1
vote
1answer
59 views

Algorithm to find most similar elements in several groups

I'd like to find an algorithm that can solve the following problem: Consider 4 groups of numbers: Group 1: [10, 100, 1000], Group 2: [101, 15, 2000], Group 3: [20, 1500, 100], Group 4: [150, 3000, ...
5
votes
2answers
2k views

An efficient way to numerically compute Stirling numbers of the second kind?

Is there an efficient way to numerically compute Stirling numbers of the second kind? An approximate (not exact) method would suffice. Something similar to the connection between factorials and gamma ...
3
votes
1answer
73 views

What is a “good enough” method of assigning values to n variables subject to basic bounding constraints while maintaining relative weights?

Given triples of $n$ floating point values $$(\min_1, \max_1, w_1), \dots, (\min_n, \max_n, w_n)$$ and a value $V$, what is a good algorithhm to assign values $v_i$ to each of the triples such that ...
1
vote
0answers
98 views

Maintain sorted ring buffer [closed]

I would like to insert elements into a ring (circular) buffer one at a time and maintain a permutation array which keeps track of the sorted elements in ascending order. To do this, I have adapted the ...
0
votes
1answer
360 views

Solving an equation in space and time using the Crank-Nicolson approach

Assume I have the following equation (light propagating in $z$-direction through the matter): $$id_zu+d^2_ru=0$$ with $u(z, r)$ being a complex wave. The time scale in this equation is $$t\equiv t_\...
4
votes
0answers
82 views

What Derivative-free optimization method should I use when my initial guess is very good?

I am trying to minimize a function where my initial guess is quite close to the minimum. I'm trying to minimize $$f(q) = \text{angle}(qw_1q*, v_1) + \text{angle}(qw_2q*, v_2) + \text{angle}(qw_3q*, ...
18
votes
1answer
530 views

Why are Octrees used for Multipole space decomposition?

In most (all?) implementations of the Fast Multipole Method (FMM), octrees are used to decompose the relevant domain. Theoretically, octrees provide a simple volumetric bound, which is useful for ...