An algorithm is a sequence of well-defined steps that defines in abstract the solution to a problem.
33
votes
1answer
908 views
Adaptive sampling for slow to compute functions in 2D
EDIT: Although I have posted an answer based on my current progress, this in incomplete. Please see the "open issues" section in the answer.
Most plotting functions in Mathematica adjust the ...
17
votes
3answers
1k views
Plotting a set of trajectories (not a vector field) in 3D
Consider a set of trajectories in 3D space, that possibly converge. By visualizing trajectories as arrows the result will look crowded as each arrowhead will be placed where the attractor is. In 2D, ...
12
votes
2answers
794 views
Simple algorithm to find cycles in edge list
I have the edge list of an undirected graph which consists of disjoint "cycles" only. Example:
{{1, 2}, {2, 3}, {3, 4}, {4, 1}, {5, 6}, {6, 7}, {7, 5}}
Each ...
20
votes
3answers
465 views
Build a refined grid based on intersecting line
I honestly have no idea where to begin with this problem. In summary, I have a 2D coarse grid with an intersecting line. For an easy example, let's assume it's a 4x4 grid.
I wish to pass through ...
22
votes
7answers
795 views
Splitting words into specific fragments
I am looking into splitting words into a succession of chemical elements symbols, where possible. For example:
Titanic = Ti Ta Ni C (titanium, tantalum, nickel, carbon)
A word may or may not be ...
18
votes
11answers
653 views
Generating an ordered list of pairs of elements from ordered lists
I have a pair of ordered lists. I want to generate a new ordered list (using the same ordering) of length n by applying a binary operator to pairs of elements, one from each list, along with the index ...
13
votes
5answers
988 views
Finding all elements within a certain range in a sorted list
Suppose we have a sorted list of values. Let's use list = Sort@RandomReal[1, 1000000]; for this example.
I need a fast function ...
8
votes
3answers
240 views
Faster Alternatives to DateDifference
I need a faster implementation of FractionOfYear and FractionOfMonth, which do the following:
Input: A time/date specified by ...
27
votes
4answers
977 views
Finding a percolation path
I would like to examine percolation on a random lattice. To be exact, I wish to find the minimum length of a 'bond' needed such that the leftmost site can be connected to the rightmost site.
Here is ...
15
votes
2answers
456 views
How can I pack circles of different sizes into a spiral?
Given a list of circles of different areas, I need to arrange them tangentially in order of increasing area and spiraling outward. An example of the type of packing I'm attempting is shown by the ...
7
votes
2answers
273 views
find subsequences of constant increase
A list like
l = {0, 1, 2, 3, 4, 5, 7, 9, 12, 13, 18, 19}
may have subsequences of constant increase, $a_{n+1} = a_n + k$.
For example:
...
41
votes
3answers
12k views
How to create new “person curve”?
Wolfram|Alpha has a whole collection¹ of parametric curves that create images of famous people. To see them, enter WolframAlpha["person curve"] into a Mathematica ...
34
votes
0answers
785 views
How to construct a treemap using non-rectangles?
I've written the standard version of a tree map (a graphic that shows nested data) and I'm looking to improve on this layout by switching to different types of polygons or perhaps circles. Can anyone ...
21
votes
3answers
382 views
Computing polynomial eigenvalues in Mathematica
MATLAB offers a function polyeig for computing polynomial eigenvalues, which appear, for instance in quadratic eigenvalue problems (see here for some applications) such as:
\begin{equation}
...
12
votes
1answer
360 views
How to extract metadata from an image of a business card?
I'm trying to digitize some documents, and I came across a very cool app called camscanner app which performs parallax transform and ocr very nicely, now I'm implementing it in mathematica...
Given ...
12
votes
4answers
672 views
Mathematica Implementations of the Random Forest algorithm
Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
14
votes
2answers
386 views
How can I speed up the classic GA for graph coloring?
I'm trying to compute the chromatic number of this graph (which is 28):
g = Import@"http://www.info.univ-angers.fr/pub/porumbel/graphs/dsjc250.5.col";
My genetic ...
12
votes
2answers
681 views
How to get actual triangles from DelaunayTriangulation[]?
The ComputationalGeometry package has a DelaunayTriangulation[] function. It returns a list of points connected to each point, ...
5
votes
2answers
207 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 $G$ ...
9
votes
2answers
169 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 ...
6
votes
1answer
232 views
How can I extend BinCounts to work on Times and Dates?
I want to extend BinCounts to work on a list of times or dates, binning them by Day, Week, Hour of the Month, Day of the Year, etc... So given a list of times and a time bin spec, I need to calculate ...
14
votes
3answers
678 views
Effective matrix power like algorithm
First example
Suppose you want to calculate the 6th power of some matrix $A$. The brute force attempt of doing this is considering
$$(((AA)A)A)A)A$$
which requires a total of 5 matrix ...
4
votes
1answer
408 views
Efficient backtracking with Mathematica
Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c ...
7
votes
1answer
164 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 ...
5
votes
1answer
94 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.:
...
5
votes
3answers
286 views
How do we solve Eight Queens variation using primes?
Using a $p_n $x $p_n$ matrix, how can we solve the Eight queens puzzle to find a prime in every row and column?
...
3
votes
0answers
122 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 ...
