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

learn more… | top users | synonyms

0
votes
0answers
9 views

FPTAS for bin packing [closed]

If an algorithm for bin packing has a guarantee of OPT(I)+log^2(OPT(I)), then there is a fully polynomial approximation scheme for this problem. I have to prove this statement, but I have no idea ...
1
vote
0answers
35 views

Finding a scalar field in order to generate a solenoidal vector from a given vector

I am working on generating a (complex) solenoidal vector field $\mathbf{A}$ from a prescribed (complex) vector $\mathbf{a}$ and the gradient of a scalar, $b$, such that $$\mathbf{A} = \mathbf{a} + ...
1
vote
2answers
76 views

How to prove time complexity of merge sort

I was asked to prove that the time complexity of merge sort is $ O(log_2n)$ but I cannot find a way to continue my method. Any help? $T(n)=2T(\frac{n}{2} )+n$ $T(n)= 2[2T(\frac{n}{4})+n] +n = ...
0
votes
1answer
32 views

MAX-SAT and MAX-cut

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
0
votes
1answer
56 views

Help me analyze the computational cost of two kinds of operations

everyone, I have a question about computational costs for a algorithm. That is: I have two vectors $u_n,\ v_n\in \mathbb{C}^N$, a matrix $A\in \mathbb{C}^{N\times N}$ (can be both sparse and dense) ...
0
votes
0answers
39 views

Proof of corollary to Chinese remainder theorem

I was puzzled regarding corollary 31.29 of the Chinese remainder theorem as presented in the chapter on number theoretic algorithms by Cormen et al. I found another person who asked the same question ...
1
vote
1answer
63 views

Efficient way to compute the cumulative weights of all subtrees rooted at each node in a tree?

I have a tree data structure (rooted, unbalanced, with unbounded branching factor), where each individual node has an associated 'weight'. For every node $n$ in the tree, I'd like to compute the ...
3
votes
1answer
57 views

Computing the (non-convex) boundary of a set of paths between two points

I have a set of paths between two fixed points (marked in red below). Each of these paths consists of an ordered series of $\{x, y\}$ points (marked in blue). I am trying to find the ordered set of ...
1
vote
1answer
41 views

Adjusting Keplerian orbits for thrust with numerical stability

I'm writing a mod for a game that models orbital physics (Kerbal Space Program, or KSP). I'm attempting to model the effects of thrust on spacecraft in certain states where the game only models them ...
6
votes
2answers
330 views

A method to determine whether a point can be contained within a circle with no neighbouring points

I have been working on a particularly challenging problem and was hoping for some guidance. Here is my problem. I have a point cloud containing millions of points. For each point in the set, I need to ...
0
votes
0answers
15 views

Max weighted subset (max sum diversification)

Given a set of elements $V$, with known cost $\pi_S$ for each subset $S \subset V$ and a monotone increasing function on the subsets $f(S)$ . I'm wondering if there is a pseudo-polynomial algorithm ...
2
votes
2answers
89 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
5
votes
0answers
130 views

Are there improved method of computing the following expression?

given a symmetric matrix $Y \in \mathbb{R}^{n \times n}$, and an arbitrary matrix $X \in \mathbb{R}^{n \times n}$, and a vector $v \in \mathbb{R}^{n \times 1}$, is it possible to compute the following ...
1
vote
1answer
100 views

What is the algorithm that matlab used in its built-in function 'pca'?

Do anyone know what is the algorithm that MATLAB used in its built-in function "pca"? I have the following data set: 148.9820 55.8438 210.2150 149.3030 56.8891 208.4280 151.4400 ...
1
vote
1answer
244 views

Patankar's algorithms for Numerical Heat Transfer and Fluid Flow

I am looking for the algorithm of Patankar (for example, SIMPLE, SIMPLER, SIMPLEC and PISO) written in Fortran for the simulation of heat transfer and fluid flow.
1
vote
1answer
40 views

What is a general method for identifying how connected parts of a binary volume are?

I have a binary volume consisting of a number of disconnected objects. (coming from a noisy, anatomic dataset) However, some of the objects are 'somewhat' connected. Picture a big cylinder and a ...
2
votes
0answers
85 views

How to get proper parameters of SPH simulation?

I'm implementing basic fluid flow simulator using SPH method basing on e.g. https://www10.informatik.uni-erlangen.de/Publications/Theses/2010/Staubach_BA10.pdf. So far I've implemented: uniform ...
1
vote
3answers
86 views

Algorithm: Extracting motion frequency from video

I was wondering if anyone knows of any algorithms or projects that can detect the frequency of a motion from a video clip. Like if I had a video of a bouncing ball with constant frequency, could an ...
1
vote
1answer
208 views

Finding optimal velocity profile using Dynamic Programming

While continuously reading about Dynamic Programming I have a problem, implementing it in a practical application. Let's assume we want to optimize our way to school which we go daily by bicycle. ...
3
votes
2answers
120 views

Finding shortest path in a time/distance map

I get a distance map output after using a Fast Marching Method. The PDE involved is the Eikonal equation which take the form : $$\begin{cases} c(x).|\nabla u| =1\\ u(x) =\phi(x) ...
1
vote
0answers
61 views

Parameter ESTimation (PEST) algorithm? Steps and purposes? [closed]

I'm reading up on the Parameter ESTimation algorithm, (Link to PEST homepage 1), and having trouble understanding the broad strokes, as I keep getting lost in null spaces, different regularized ion ...
1
vote
2answers
70 views

How to measure trajectory regularity?

I have two animal running trajectories. A regular one with repeated back and forth running between point A and B, like the one on top in the figure. The other one is very irregular, animal paused and ...
0
votes
0answers
33 views

Algorithm for porosity based CFD mesh

I am writing the pre-processing program for a porosity based CFD project. I have a mesh made of cubes, and need to import an object (a stl file: triangular mesh, not solid) over it. The cubes will ...
1
vote
1answer
93 views

How to minimize the artefact of a cartesian to polar transform followed by a polar to cartesian transform?

I'm transforming cartesian images into polar images. (x,y) => (angle, radius) I fill the polar image by iterating on each of its pixels and filling them by doing the reverse polar transform. For a ...
4
votes
1answer
101 views

Numerically compute one-to-one mapping

I have a set of points defined by their coordinates $(x_1,y_1)$ after changing some parameters of the problem I obtain a second set of points defined by their coordinates $(x_2, y_2)$. There exists a ...
1
vote
1answer
53 views

Appropriate algorithm for (non-linear) ODE with integral equilibrium constraint: collocation?

I have a problem of the following structure: For some scalar $g$, functions $F(z)$ and $h(z)$ defined on $[0,\bar{z}]$ , and a non-linear operator $\phi(F,z)$ (in reality, $F$ and $h$ are vector ...
1
vote
1answer
55 views

Algorithm for distributing members over activites (with individual preferences)

So in my school we have a day where everybody participates in different activities. Each projects can have like 10 members. The whole day is divided in 2 or 3 different blocks, in which the pupils ...
0
votes
1answer
64 views

Finding roots without knowing much about the function

Consider solving numerically for roots: $( x_0, y_0): f(x_0, y_0) = 0, g(x_0, y_0) = 0$ where you only know that f, g continuously differentiable but the theoretical differentiation is not a ...
2
votes
0answers
46 views

Algorithm for optimizing graph interconnectivity

I have a partiuclar kind of graph problem and (not having a background in graph algorithms) I would like to know how this kind of problem is called in the literature and what algorithms exist for ...
0
votes
0answers
16 views

Generation of symmetric groups

I've been trying to make an algorithm to generate symmetric groups in order to create graphics like the ones shown here. I've programmed circular and dihedral groups so far, but could someone help me ...
9
votes
0answers
121 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 ...
1
vote
1answer
45 views

How to compute the weight matrix for tomography applications?

I am trying to compute the weight matrix for a set of straight ray paths through a reconstruction region. Ideally, I would like to be able to do this for both a rectangular grid region, where each ...
0
votes
0answers
66 views

Algorithm for Octree for nearest neighbor seach

Problem Statement: To find the nearest GRID ID of each of the particles using Octree. I have a system of particles(~6k, movable, Fig 1) for which I need to check which grid point (rigid; in ...
0
votes
0answers
50 views

Algorithm to explore a 3D scalar potential

I have to write an algorithm/code to reconstruct an unknown 3D scalar potential $ V(\mathbf{r})$ up to a specified threshold $E_c$ (assume that the potential is monotonic) The problem has the ...
10
votes
1answer
505 views

What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?

I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...
0
votes
2answers
188 views

How can I create a computational model of the human eye?

I need to create a program that can simulate the optical system of the human eye. The input will be any image, the output would be the image that is projected onto the retina. I need it to be as ...
9
votes
3answers
651 views

Is there a complexity between $O(n)$ and $O(n \log n)$ [closed]

Is there a complexity degree that is bigger than $O(n)$ and smaller than $O(n \log n)$?
1
vote
0answers
41 views

Computing a description of a set of lattice points

I have an infinite subset $S$ of $\mathbb{N}^k$ which I know (or at least strongly suspect) is a finite union of regions, each of which is defined by finitely many linear equalities and inequalities ...
3
votes
1answer
121 views

Examples of high polynomial order complexity

I was reading Twenty Questions for Donald Knuth and was intrigued by Knuth's argument in question 17 for why he suspects P=NP. In the discussion he asks why you couldn't have an algorithm bounded by a ...
2
votes
0answers
40 views

Algorithms for adding hydrogens on a molecule

I want to add hydrogens to some linear polymer molecules (polyethylenes). I know some working methods like using PyMOL internal function h_add. This method works, but hydrogens are added at distances ...
0
votes
0answers
32 views

Matching signals in time domain

I would like to ask about methods to match one dimensional discrete signals to given templates. So far I have studied the basics of DTW algorithm, but I do not know if this is the optimal method. The ...
1
vote
1answer
216 views

Is there always a linear iterative alternative to a recursive iterative process? [closed]

This may very well be a silly question but I'm trying to cement my understanding of the material in the SICP (http://goo.gl/QXrbtV). My intuition (common sense) says yes, but wondering from a ...
1
vote
2answers
138 views

How to get ODE solution at specified time points?

The code below basically illustrates my problem. It is a test code for a pendulum. I solve it using a method suggested on ...
1
vote
1answer
134 views

Most memory-efficient way to store a list of numbers

My problem deals with a large $n \times m$ matrix from which I extract and store several square $k \times k$ submatrices. The original matrix may be very large, and I may need to store many thousands ...
0
votes
1answer
197 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 ...
1
vote
0answers
72 views

Solving “virus”, a flash game, in the least amount of attempts

We am currently working on a project related to computational optimization, in which I have tasked myself with calculating the most efficient solution to one of the game's levels. Link to the flash ...
0
votes
0answers
115 views

Dijkstras algorithm-> shortes path problem

Hi i have problem understanding shortest path computation when Dijkstra’s algorithm is applied. Given the graph as depicted below the shortest path from A to G is 42 and that corresponds to ...
3
votes
1answer
217 views

Large binary programming problem

I have 10000 variables (each of them is binary), vector of positive coefficients and a matrix A (10000*10000), if Aij is 1, then ith and jth variables can take 1 simultaneously, if it's 0, then it's ...
1
vote
0answers
24 views

What's the most efficient way to calculate the Wiger quasiprobability distribution?

I want to calculate the Wigner quasiprobability distribution function of a particular wavefunction. The definition suggests a few straightforward ways of calculating it, but I was wondering if there's ...
3
votes
3answers
180 views

Efficient solver for a symmetric tridiagonal system where the upper/lower diagonals are offset

I'm looking for an efficient way to solve a symmetric tridiagonal system $Mx = d$, where the upper and lower diagonals of $M$ are offset from the main diagonal by $k$ rows/columns: $$ \begin{bmatrix} ...