An algorithm is a sequence of well-defined steps that defines in abstract the solution to a problem.
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2answers
48 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
42 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 ...
4
votes
0answers
70 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 ...
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votes
1answer
60 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 ...
4
votes
1answer
82 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.:
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vote
0answers
74 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
154 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
117 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 ...
4
votes
2answers
173 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
60 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
63 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 ...
6
votes
1answer
108 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 ...
4
votes
1answer
173 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:
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7
votes
2answers
217 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, ...
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votes
4answers
565 views
Mathematica Implementations of the Random Forest algorithm
Is anyone aware of Mathematica use/implementation of Random Forest algorithm?
