My professor said that I should find a way to find the number of triangles in a graph. I have a problem what graph should I used but my professor suggested that I must first find a way to count the triangles in a graph. I've searched it through Google and I found that there's an algorithm in counting the triangles in a graph but I don't understand much about it because I'm not a ComSci (Computer Science) student. And I also found that I can count the number of triangles by matrix. (1/6)(A)^3. It's a trace of A. So... what I'm asking right now is another idea of finding the number of triangles in a graph. Thank you if I got an answer!
A simple approach is to visit each node and try each path from it that has length 3. If it end at the start-node it will be a triangle.
This is not optimal considering time consumption, but it is simple.
Related
I am trying to implement Branch and Bound approach to the edit distance algorithm. I can't find any hints over internet to start with. Can anyone help me to get into the track of the algorithm.
My apologies for posting this as an answer, I wanted to add it as just a comment, but I don't have sufficient reputation to add comments.
Try to approach your literature search of this subject rather in the context of the graph similarity problem than for the edit distance algorithm; the prior is a more general and well-studied problem which the problem of finding the minimum edit distance fall under. The strings in any instance of your edit distance problem can be described as simple directional graphs, and the operations of insertion/deletion and substitution in the edit distance algorithm has similar operations in the graph similarity problem (e.g., insertion of vertices and edges/deletion of vertices and edges/changing labels on edges and so on).
i know about the traveling salesman problem, but is there any other algorithm/problem which better fits my needs/description? I need to describe my problem with the help of such a mathematical description.
I have a set of nodes with known start- and endpoint. So i just need to calculate the shortest way to visit all the three points between that two. Dijkstra and similar algorithms try to find the shortest path between two points, so here they probably won´t visit all points between. Or is there a algorithm which finds shortest way and visit all points between two points?
You can achieve it using Ant colony optimization algorithms. Refer Ant colony optimization algorithms.
The complexity of the general case of your problem is at least as high as for the Travelling Salesman problem. Just imagine the case where your two endpoints are basically in the same position, then your problem becomes equivalent to the Travelling Salesman.
If you never expect more than five points in your graph though, do you really need to bother with fancy algorithms? You could just do an exhaustive search for the best solution. Since the only decision is the order in which you visit the three points in the middle, you will only have to test 3! = 6 different paths. Even if I misunderstand you and you want the overall shortest open path that visits all nodes, that would still only be 5! = 120 different paths to test (60 if distances are the same in both directions).
I have a set of 3D points which numbers up around 1 million points. I am looking to visualise these with matlab.
I have tried the following functions:
plot3
scatter3
But they are both very sluggish. Is there a more efficient way to visualise this level of points in matlab? Maybe a way to mesh the points?
If not can anyone suggest a plug-in or even a different program for visualising 3D points?
You're going to run into efficiency issues no matter what plugin/program you use if you want all million+ points to show up in a plot. My suggestion would be to downsample. Use the plot3 or scatter3 function on every other point, or every nth point, until you get a figure that is not sluggish. As long as the variance in your data isn't astronomical, downsampling a little bit shouldn't affect the overall distribution of points (given that you have a million+ points). And any software that is able to display that much data without being sluggish is most likely downsampling/binning or using some interpolation technique to do so (so you might as well have control over it).
fscatter3 from the file exchange, does what you like.
Is there a specific reason to actually have it display that many points?
I Googled around a bit and found some people who have had similar issues (someone suggested Avizo as an alternate program but I've never used it):
http://www.mathworks.com/matlabcentral/newsreader/view_thread/308948
mathworks.com/matlabcentral/newsreader/view_thread/134022 (not clickable because I don't have enough rep to post more than two links)
An alternate solution would be to generate a histogram if you're more interested in the density of the data:
http://blogs.mathworks.com/videos/2010/01/22/advanced-making-a-2d-or-3d-histogram-to-visualize-data-density/
I you know beforehand roughly the coordinates of the feature you are looking for, try passing the cloud through a simple pass-through-filter, which essentially crops your point cloud. I.e. if you know that the feature is at a x-coordinate > 5, remove all points with x-coordinate < 5.
This filter could for the first coordinated be realized as
data = data(data(1,:) > 5,:);
Provided that your 3d data is stored in an n by 3 matrix.
This, together with downsampling, could help you out. If you still find the performance lagging, consider using something like the PCD viewer in PointCloudLibrary, check half way down the page at
http://pointclouds.org/documentation/overview/visualization.php
It is a stand alone app you could launch from matlab. I find it's performance far better than the sluggish matlab plotting tools.
For anyone who is interested I ended up finding a Point cloud visualiser called Cloud Compare. It is extremely fast and allows selection and segmentation as well as filtering on point clouds.
I want to find the K-farthest neighbors in a given undirected weighted graph (the graph is given as a sparse weight matrix, but I can use an representation advised).
Just to make sure the problem is well-defined: I want to find k nodes which have maximal distance from one another.
Solutions that are close to the optimal set are also ok - I just need it to find some farthest points in a mesh :)
Assuming you are just looking for a decent solution I would recommend a simple solution similar to the "furthest insertion" starting position for the travelling salesman problem:
Add 1 point to the empty set, preferably one in the corner or in the edge (Of course you can just try all of them)
Add the furthest point to the set (increase the distance most from current points in set)
Keep repeating the previous step untill there are k points in the set
It will not be optimal but probably not very bad.
If you want to improve on this you could use a heuristic to improve on the result, for example:
Consider the set with point 1 to j left out, j
Try all possible points to substitute these j points
record best possible solution
Consider the set with point 2 to j+1 left out
etcetera
Furthermore if k is not too large, say less than 5, and the total amount of points is not too large, say less than 100, it will probably be easier to just calculate all possible combinations. This is assuming that the norm calculation can be done efficiently.
EDIT:
Once you know you want to implement this the regular way to continue is find something similar and edit it a bit to suit your needs. If you scroll down on this page you should find an example of furthest insertion. Editing it to follow your measure of 'far' should be managable.
http://snipplr.com/view/4064/shortest-path-heuristics-nearest-neighborhood-2-opt-farthest-and-arbitrary-insertion-for-travelling-salesman-problem/
I have a sequential collection of points in X,Y and I'd like to "trace" these into a set of bezier curves. Could any open source bitmap to vector tracing algorithm or library be used for this?
This depends on what you want to accomplish. If you want to see the 'best fit' curve, or at least a rough approximation, you should use a b_spline. A b_spline will fit itself 'inside' the points it is given. For going through the points in question I would generally use a Catmull-Rom spline which, when given points 1,2,3 will pass through point 2 with slope equal to the slope between points 1 & 3.
Sample Code:
http://willperone.net/Code/spline.php
Explanation of the algorithm:
http://steve.hollasch.net/cgindex/curves/catmull-rom.html
You want to use piece-wise b-spline curves rather than beziers if you want the curve to pass through an existing set of points.
There's tons of code on the web for doing this.
This is an older question, but I found it because I need an algorithm for autotracing coordinates as they're being drawn, and found this SO post through Google. It looks like for this particular question no one's mentioned Potrace (small wikipedia article on it here), which is pretty much literally what the original question was asking for, and is open source with several ports as well as the papers that describe its function freely available.