Questions tagged [algorithms]

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

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One to Many Assignment Problem where agents can't be assigned the same task if they share a trait

In the one to many assignment problem, many agents can be assigned to a task. In my problem, I want to assign many agents to a task, but for all of the agents assigned to that task, they must share a ...
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2answers
122 views

Fast algorithm for computing the similarity between two arrays

Suppose there are two arrays (They have the same length), I want to give a quantitative description about the similarity between them. I define a formula like this, which means we can shuffle them ...
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1answer
43 views

Is there an efficient algorithm for calculation of continued fraction expansion from decimal digits?

Suppose to calculate the continued fraction expansion of $\pi$, the common-sense algorithm would be to take the decimal part, perform inversion, which will give the next term as integer part, and the ...
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1answer
110 views

Numerically stable and fast sum of last K elements in sequence

Suppose I have a long, possibly infinite, sequence $x := [x_1, x_2, ...]$, and I want to use it to compute another sequence $y:=[y_1, y_2, ...]$ where each element is the sum of the last K elements of ...
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Efficient way to find eigenvalues of complex symmetric matrix with real off-diagonal elements

My goal is to find all eigenvalues (and eigenvectors) in a given range of magnitudes of a complex symmetric matrix with real off-diagonal elements (only diagonal elements are complex). Currently I'm ...
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Alternatives to breadth-first-search in 3D grid cluster detection?

I've got a question about a good way to find the quickest algorithm for my problem: problem: I've got a 3D cubical grid containing voxels that are either 1 or 0. It is stored as a flattened array. If ...
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Solving a 2-time Volterra integro-differential equation

In non-equilibrium field theory one usually encounters the so called Kadanoff-Baym equations, which are Volterra integro-differential of 2 times $$ i \partial_t f(t,t^\prime) = h(t) f(t, t^\prime) + \...
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Evaluating integral $F(r_2) = \frac{1}{r_2^n} \int_0^{r_2} r_1^n f(r_1)\ \mathrm{d}r_1$ without growing instability

I have the following expression to be numerically integrated in a vector-based library (e.g. numpy, MATLAB, etc), $$ F(r_2) = \frac{1}{r_2^n} \int_0^{r_2} r_1^n f(r_1)\ \mathrm{d}r_1, $$ where $n$ is ...
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SHREC 2010 Descriptors

I will appreciate if I may find someone how can clarify for me the part regarding the quality of feature descriptor, shown in the figure below: and this screenshot is from the article: SHREC All my ...
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1answer
57 views

Evaluate 3D Shape Descriptor

I'm trying to create my own 3d shape descriptor, the idea is that how I may evaluate how much my descriptor is well and good? What I checked is that they evaluate descriptors through shape matching, ...
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0answers
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Computation of Troullier-Martins pseudowavefunctions

The computation of Troullier-Martins pseudowavefunctions has been described in [1]. The pseudowavefunction $R^{\textrm{PP}}_l$ is defined by $$ R^{\textrm{PP}}_l(r) = \left\{ \begin{array}{ll} R^{\...
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3answers
337 views

Should benchmarkings be done at all? What is the point?

I am reading a paper which compares algorithm A versus algorithm B. It shows that algorithm A is faster than algorithm B via benchmarking that shows the CPU time. What is the point of this? Any ...
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0answers
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How to approach geographic data interpolation by distance?

let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order. Now I'm ...
3
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1answer
68 views

Calculate Transformation Matrix between two sensors

My question is if I can calculate the transformation matrix between two sensors. Each sensor provides a $4\times 4$ matrix for every timestep recorded. The sensors are moving and have some noise in ...
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What is Voronoi particle tracking?

I've been trying to track this down, but google is giving paywall papers that don't appear to be directly related to computational science, or simply don't explain the source algorithm. There's an ...
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1answer
206 views

Understanding butcher tableau when it comes to implicit methods

I've been learning about butcher tables and am having some difficulty understanding how to translate them when it comes to implicit methods. Specifically, I'm looking at backwards Euler: \begin{array}...
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What exactly is the cause(s) of blow-up for too-large step size in a method like RK4?

I have been working on creating a few home-made numerical methods, and I am using them to visualize text-book problems from my Strogatz dynamics textbook. It feels like a good way to learn numerical ...
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Hybrid Ellpack-Itpack (ELL) + COO Sparse Matrix Representation decomposition threshold

Hybrid ELL-COO sparse matrix representation can be done as in the picture, I was looking intensively, however I couldn't find out what is the threshold of decomposing the original matrix into ELL part ...
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1answer
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Efficient computation of leading eigenvector of a matrix product of the form $ADA^T$, where $D$ is diagonal

Let $A=[A_1|\ldots|A_m] \in \mathbb R^{n \times m}$ with $n \gg m \gg 1$ and $D=\text{diag}(d_1,\ldots,d_m)$ where $d_1,\ldots,d_m > 0$, and consider the $n\times n$ positive-definite matrix $X=\...
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solving electron motion in undulator by Boris method

I am trying to use Boris scheme to solve the electron trajectory in undulator. The undulator field I used is: $$B_x = b_0\sin(2\pi \tfrac{z}{\lambda_u})$$ where $b_0 = \dfrac{2\pi c_{0}K}{q m_{e} \...
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1answer
72 views

Weighted moving variance

i have a time-series and, in analogy with exponentially weighted moving average, i would like to compute the exponentially weighted moving standard deviation or variance in an efficient, numerically ...
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1answer
48 views

Dealing neighbor list in NVT Monte Carlo (MC) simulation

I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction. I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...
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2answers
118 views

Efficient algorithm to decide if a graph is a cactus?

A cactus is a connected graph in which every edge belongs to at most one simple cycle. How should one modify the Depth First Search algorithm to obtain an efficient algorithm that determines if a ...
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1answer
152 views

Fast algorithm for computing cofactor matrix

I wonder if there is a fast algorithm, say ($\mathcal O(n^3)$) for computing the cofactor matrix (or conjugate matrix) of an $N\times N$ square matrix. And yes, one could first compute its determinant ...
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1answer
31 views

How is the D value being updated at simple RRT algorithm?

I am studying the following lecture (image) regarding 5 iterations of the simple RRT algorithm. I am trying to understand how each value is being updated regarding each iteration. I have figured out ...
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A preconditioner for self-consistent iteration

I tried to derive a preconditioner for self-consistent iteration similar to section IX in arXiv:0804.2583. For simplicity, consider here only one orbital (one or two electrons) systems. Suppose that ...
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1answer
201 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, ...
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1answer
45 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 ...
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1answer
74 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, ...
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1answer
80 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 : ...
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0answers
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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 ...
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1answer
128 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 ...
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3answers
151 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 ...
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0answers
37 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 ...
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1answer
75 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 ...
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1answer
74 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 ...
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0answers
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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 ...
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0answers
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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 ...
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1answer
20 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 ...
3
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1answer
60 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 ...
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0answers
590 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 ...
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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, ...
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1answer
61 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 ...
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1answer
87 views

Pivoting in Block LU

What are common methods to choose pivot blocks in Block LU (for non-SPD/non-Diagonally Dominant Matrices)?
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0answers
80 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?
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1answer
168 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 ...
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0answers
187 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 ...
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0answers
81 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 \...
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0answers
199 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 ...
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1answer
63 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, ...

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