An algorithm is a sequence of well-defined steps that defines in abstract the solution to a problem.

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6
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2answers
137 views

Algorithm in RandomChoice[{w1,w2,…}->{e1,e2,…},n]?

I wonder if someone happens to know the actual algorithm implemented in the particular overload of RandomChoice that handles explicitly presented discrete ...
0
votes
1answer
225 views

Generate encoding from nested list

Taking reference of Huffman code algorithm, ...
6
votes
2answers
278 views

Generated Numbers under a constraint?

Let's say I have five four dimensional vectors $p_i^\mu=(p_i^1,p_i^2,p_i^3,p_i^4)$ with $i=1,2,3,4,5$. Now, I want to fill the entries of these vectors ($4\cdot5=20$ in total) with some numbers, but ...
3
votes
3answers
316 views

Fastest way to check if an expression contains all symbols from a list

I need to execute this function thousands of times, and the faster, the better. I came up with two versions, but wanted to see if you can come up with an even faster way. Is there a better way? I use ...
4
votes
3answers
335 views

Creating a function with integral zeroes of the 0th, 1st, and 2nd derivatives

I would like to be able to randomly generate functions, each of which satisfies $f : [-10, 10] \rightarrow [-10, 10]$ All the zeroes, critical points, and inflection points have an integral ...
3
votes
2answers
154 views

Checking whether a number can be composed from the cube of its digit

How to check whether or not the sum of the cube of each digit of a number is equal to the number itself? In the following code, I tried to return the number in question whenever it matches the ...
5
votes
1answer
202 views

Using mathematica to discover algorithms?

In Steven Wolfram's blog entries, he discusses using mathematica to discover algorithms. I have tried several different google searches for papers on such topics, and have found none. I suspect this ...
7
votes
5answers
1k views

Check if a matrix is Positive Semidefinite

I have a question concerning the check whether a given matrix is positive semidefinite or not. In mathematica the function PositiveDefiniteMatrixQ[m] tells me ...
5
votes
1answer
279 views

What algorithm and tools should I use to search a data set for the point nearest to a given point?

I have about 1,000,000,000 points, which are the longitudes and latitudes of some places in a city, formatted like this: $(106.1231233,41.43234234)$. I also have about 20,000 points which are the ...
2
votes
2answers
172 views

Write 199319989756262759279209 = 5x + y, where x and y are integers

$\frac{199319989756262759279209}{5} $ = $ 3.9864\times 10^{22}$ according to Mathematica, but I would like to see this number exactly in decimal form (not in scientific notation). I'm attempting to ...
21
votes
3answers
1k views

Generate a Random Polygon

Does some package exist with a function that takes a parameter $n$ and generates a random 2D $n$-sided simple polygon (convex or non-convex), possibly within a certain bounding box? It does not ...
5
votes
2answers
213 views

Parallelizing or optimizing a script for calculating the size of all pairwise intersections between collections of sets

I need to speed up or parallelize an operation that looks essentially like this: ...
6
votes
1answer
292 views

Behavior of Graphics`Mesh`InPolygonQ with self-intersecting polygons

Playing around with some of the answers in the question How to check if a 2D point is in a polygon? I noticed that: Graphics`Mesh`InPolygonQ[poly,pt] Displays ...
1
vote
4answers
288 views

Calculating the median difference between elements with a (particular pair) of consecutive integer indices residing in the same sublist

NOTE: I formally made a serious mistake in the first example provided. pointLists[[1]] had an extra element, and we should have a guarantee that ...
6
votes
5answers
536 views

A fast way to calculate the median difference between pairs of elements

I have a list of coordinate pairs, take for example the following list of three pairs: ...
1
vote
2answers
636 views

Faster way to test if an expression equals zero

I want to test if expressions (mix of variables, functions and numbers) are zero valued, as fast as possible, and PossibleZeroQ is sometimes very slow. One solution ...
2
votes
2answers
360 views

Is there a way to parallelize the convolution component of EdgeDetect?

Provided an image like - test = Import["http://upload.wikimedia.org/wikipedia/commons/d/d5/Sunflowers.jpg"] We can run ...
1
vote
1answer
193 views

Efficiently determining if a morphological component overlaps a polygon with vertices at real number coordinates

I have a list of morphological components $m$, a set of vertices for a polytope $P$ (at real number coordinates), and I'd like to be able to calculate a list of morphological components $m'$ that ...
14
votes
2answers
579 views

Implementing an algorithm for finding the largest circle that contains a single point in a set (and no other point)

This question concerns the implementation of an algorithm proposed by Rahul Narain on a former question of mine that was migrated to math.stackexchange: ...
4
votes
3answers
348 views

Computing the mean difference between elements in a list with index $i$ and the closest elements with index $(i+1)$

I have a list that looks like this: preprocessedList = {{1,5.3},{1,5.566},{1,1.4322},{2,3.443543},{2,3.444},{3,0.1223},{4,1.3243},{4,1.554343}} Each element in ...
15
votes
3answers
696 views

How to partition a list to make each subset's size equal and mean as close as possible

Suppose we have 3 lists each with 18 numbers like this: ...
0
votes
0answers
279 views
20
votes
1answer
475 views

Underlying Algorithms for List Manipulation Functions

Does anyone know, or know of a link for the underlying algorithms used for list manipulation functions? Specifically: Union with and without the ...
9
votes
2answers
269 views

Partitioning a superset of coordinates into subsets that generate continuous curves

Consider the data set corresponding to recorded trajectories for a particle: ...
6
votes
2answers
399 views

Pruning elements in an array based on the existence of similar elements in adjacent arrays

Imagine I have a series of particles floating around in $\mathrm{R}^3$, where, at any given time, particles can pop into and out of existence. Here, for some number of time points, $(t_1, \dots, ...
2
votes
3answers
111 views

Reversibly merging sets of $k$ adjacent elements in an array

Say I have an array of the form: ExampleArray = {{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}, {9}, {10}, {11}, {12}}; I'd like to be able to reversibly merge sets of ...
2
votes
1answer
381 views

Finding a fixed vector which minimizes the pairwise distance between noisy elements in two unordered arrays

Let $A$ and $B$ be two sets of $d$-dimensional coordinates of comparible (though not necessarily equal length). For example, here we can set $d = 3$ and have normalized values like: ...
1
vote
1answer
158 views

Finding a mapping between elements in two lists that satisfy some criterion (such as being less than threshold Euclidean distance apart)?

I have two lists of $d$-dimensional coordinates, for example setting $d=3$ we might write: ...
4
votes
2answers
431 views

Efficiently determining the largest minimum cost to travel from a fixed source to an arbitrary sink in a weighted graph

Let $v_i$ be a vertex in a graph $G$ with vertices $(v_1,...,v_N) \in V$ and edges $(e_1,...,e_M) \in E$ with associated weights $(w_1,...,w_M)$. Let $v_s \in V$ be specified vertex in the graph. In ...
0
votes
1answer
169 views

Returning lists of pixels connected through their Moore neighborhoods

I have a binarized image in Mathematica 9, and I would like to generate a list of coordinates for clusters of pixels connected through their Moore neighborhoods, e.g. ...
1
vote
1answer
482 views

Understanding the computation of the geometric median

In the Wolfram Demonstration Fermat Point for Many Points, it appears that the geometric median is being calculated for an arbitrary set of five manipulable points. How might one extend this ...
3
votes
2answers
2k views

How to linearize an expression automatically?

I would like to automatically linearize some long equations in the scope of variational calculus. Here follows an example of what I need to do : Given two variables $a_1 = q_1 + \delta q_1$ and $a_2 ...
14
votes
1answer
255 views

Baffling increase in runtime

Background of my question I discovered Project Euler today, and decided I would work through the problems in Mathematica. I became obsessed with the first problem, which is essentially "sum all the ...
7
votes
2answers
290 views

What is the underlying algorithm for GroupElementToWord?

What algorithm is Mathematica 9 using for GroupElementToWord[group, g]?
1
vote
1answer
156 views

How can I stop DiscreteMarkovProcess[] from relabeling vertices?

I'm attempting to calculate the mean first passage time between two vertices, $v_1$ and $v_2$, provided some undirected graph $G$. However, I noticed that running the following script: ...
0
votes
2answers
137 views

How can I efficiently and uniformly sample the set of vertices a fixed edge-wise distance away from a chosen vertex?

I have a large graph $G$, which may be either directed or undirected. How would I use DepthFirstScan[] or BreadthFirstScan[] to ...
2
votes
0answers
218 views

Fast calculation of commute distances on large graphs (i.e. fast computation of the pseudo-inverse of a large Laplacian / Kirchhoff matrix)

I have a large, locally connected and undirected graph $G$ with $\approx 10^4$ vertices and $\approx 10^5$ to $\approx 10^6$ edges. Moreover I can bound the maximum vertex degree as $Q_{max}$. I ...
5
votes
1answer
414 views

Counting paths of a certain length between a source and sink vertex

I have a graph $G$, which may be directed or not, and I was wondering if there was an efficient way of using, say, BreadthFirstScan[] and FindShortestPath[] to count the number of paths between some ...
0
votes
1answer
125 views

Can I force a function to quit and return some value after a certain amount of time has passed during its evaluation?

Imagine I provide some random input to function like FindInstance[], and I observe that, despite the existence of good solutions, the function will, with some ...
6
votes
1answer
173 views

Why is FindInstance failing when I relax a set of constraints?

I'm attempting to use FindInstance to generate coordinate sets for plausible triangles with edge length distance constraints. E.g.: ...
3
votes
0answers
581 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
7
votes
1answer
265 views

Making FindShortestPath a little bit sloppy [duplicate]

I have a dense graph, and I'd like to find multiple "almost shortest" paths from a source vertex, $v_s$, to a sink vertex, $v_s$, on an undirected graph $G$. How can I repeatedly run ...
4
votes
1answer
206 views

Is there a fast way to trilaterate a point?

I have a point in 2D or 3D space at an unknown coordinate, $p_0$, and I'd like to determine its position using distances from known coordinates $(p_1, p_2, p_3)$. Beyond using ...
7
votes
2answers
308 views

Is there something akin to “SubgraphIsomorphismQ” in Mathematica 9?

Provided two unlabeled graphs, $G$ and $H$, I would like to test where $H$ is a subgraph of $G$. In other words, I'd like to test whether we can prune some fixed number of vertices or edges from $G$ ...
2
votes
1answer
135 views

Is it possible for me to explicitly specify a point list for SpatialGraphDistribution?

The function RandomGraph[SpatialGraphDistribution[n, r]] generates a random geometric graph over $[0,1]^2$ where vertices are connected if they are within a ...
2
votes
1answer
156 views

Determining whether two k-chromatic graphs are equivalent (not simply isomorphic) using IsomorphicGraphQ?

In a previous question of mine, I asked whether Mathematica's built-in routines could determine an isomorphism for two $k$-chromatic graphs, Determining whether two $k$-chromatic graphs are isomorphic ...
12
votes
2answers
396 views

Determining whether two $k$-chromatic graphs are isomorphic (respecting vertex coloration)

Consider the case where I have two $k$-chromatic graphs $G_1$ and $G_2$, i.e. two graphs where individual vertices can be colored with one of a set of $k$ total colors, and I would like to determine ...
5
votes
1answer
818 views

Efficient method for inverting a block tridiagonal matrix

Is there a better method to invert a large block tridiagonal Hermitian block matrix, other than treating it as a ordinary matrix? For example: ...
8
votes
2answers
479 views

Finding all points of period n in an iterated map

I'm trying to implement an algorithm of Jenkinson and Pollicott to calculate the Hausdorff dimension of a Julia set for the map $f_c : z\mapsto z^2 + c$. It's described on page 40 of their paper, ...
24
votes
5answers
2k views

Mathematica Implementations of the Random Forest algorithm

Is anyone aware of Mathematica use/implementation of Random Forest algorithm?