I have been searching some information about Dijsktras algorithm, and I found that its alway beeing applied to this kind of graph. Is it possible to use Dijkstra if I have tree/heap structure of graph ?
Dijsktras's algorithm is a single-source shortest path algorithm for general graphs with weighted edges. As long as your data structure is a graph with quantifiable edge weights (can be all 1), there should be no reason why it does not work.
Related
i have a social network described as edges in a file. I used graph based clustering algorithms to find dense parts of the graph. However there is also vector based clustering which i need to apply to the data i have, but i can not find any context to this. I have also information about each node considering their features. I think using vectors containing the features of each user makes no sense here. For example k-Means would calculate the distance between user u1 with his feature vector v1 = [f1,f2,f3,..] and user u2 with its feature vector v2 = [f1,f2,f3,...]. However both vectors would have binary values depending on which feature the user has. Additionally i have a matrix with the users on one axis and the features on the other, where the user is able to set permission.
My Question is now, how i can make use of k-means, dbscan etc. in the context of this topic.
Best wishes.
Many algorithms can be modified to allow being used with distances for binary features. For example k-means can be modified for binary data: k-modes.
But I don't think it will do anything useful on your data.
You approach to this problem is bad: don't first decide the algorithm, then try to make it run. You are then bound to solve the wrong problem. Instead, formalize the problem first, in mathematics, what a good clustering would be. Then identify the appropriate algorithm by it's mathematical ability to find a good solution to this objective.
I am trying to solve this problem by using of Monte-Carlo Flooding algorithm. As result I receive set of semicircles (the picture below), but the requested solution is for trapezoid like polygons. Please, can you suggest me an algorithm by which I will be able to transform this semicircles in polygons?
First, you extract your pieces as contours, using Suzuki-Abe algorithm (Suzuki, S. and Abe, K., Topological Structural Analysis of Digitized Binary Images by Border Following. CVGIP 30 1, pp 32-46 (1985)). You'll get all contours out of your image as they are produced.
Then, you approximate contours into polygons using Ramer-Douglas-Peucker algorithm.
THere is well-known library which does it all - OpenCV, see link for details https://docs.opencv.org/2.4.13.2/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html
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 Dijkstra's agorithm, Floyd-Warshall algorithm and Bellman-Ford algorithm for finding the cheepest paths between 2 vertices in graphs.
But when all the edges have the same cost, the cheapest path is the path with minimal number of edges? Am I right? There is no reason to implement Dijkstra or Floyd-Warshall, the best algorithm is Breadth-First search from source, until we reach the target? In the worst case, you will have to traverse all the vertices, so the complexity is O(V)? There is no better solution? Am I right?
But there are tons of articles on the internet, which talk about shortest paths in grids with obstacles and they mention Dijkstra or A*. Even on StackOverfow - Algorithm to find the shortest path, with obstacles
or here http://qiao.github.io/PathFinding.js/visual/
So, are all those people stupid? Or am I stupid? Why do they recommend so complicated things like Dijkstra to beginners, who just want to move their enemies to the main character in a regular grid? It is like when someone asks how to find the minimum number in a list, and you recommend him to implement heap sort and then take the first element from sorted array.
BFS (Breadth-first search) is just a way of travelling a graph. It's goal is to visit all the vertices. That's all. Another way of travelling the graph can be for example DFS.
Dijkstra is an algorithm, which goal is to find the shortest path from given vertex v to all other vertices.
Dijkstra is not so complicated, even for beginners. It travels the graph, using BFS + doing something more. This something more is storing and updating the information about the shortest path to the currently visited vertex.
If you want to find shortest path between 2 vertices v and q, you can do that with a little modification of Dijkstra. Just stop when you reach the vertex q.
The last algorithm - A* is somewhat the most clever (and probably the most difficult). It uses a heuristic, a magic fairy, which advises you where to go. If you have a good heuristic function, this algorithm outperforms BFS and Dijkstra. A* can be seen as an extension of Dijktra's algorithm (heuristic function is an extension).
But when all the edges have the same cost, the cheapest path is the
path with minimal number of edges? Am I right?
Right.
There is no reason to implement Dijkstra or Floyd-Warshall, the best
algorithm is Breadth-First search? Am I right?
When it comes to such a simple case where all edges have the same weight - you can use whatever method you like, everything will work. However, A* with good heuristic should be faster then BFS and Dijkstra. In the simulation you mentioned, you can observe that.
So, are all those people stupid? Or am I stupid? Why do they recommend so complicated things like Dijkstra to beginners, who just want to move their enemies to the main character in a regular grid?
They have a different problem, which changes the solution. Read the problem description very carefully:
(...) The catch being any point (excluding A and B) can have an
obstacle obstructing the path, and thus must be detoured.
Enemies can have obstacles on the way to the main character. So, for example A* is a good choice in such case.
BFS is like a "brute-force" to find the shortest path in an unweighted graph. Dijkstra's is like a "brute-force" for weighted graphs. If you were to use Dijkstra's on an unweighted graph, it would be exactly equivalent to BFS.
So, Dijkstra's can be considered an extension of BFS. It is not really a "complicated" algorithm; it's only slightly more complex than BFS.
A* is an extension to Dijkstra's that uses a heuristic to speed up the pathfinding.
But when all the edges have the same cost, the cheapest path is the path with minimal number of edges?. Yes
If you really understood the post that you linked, you would have noticed that the problem they want to solve is different than yours.
I am dealing with undirected graph. I need to find all possible acyclic paths within a graph:
with G(V,E)
find all subsets of V that are acyclic paths
I am using either python scipy or matlab - whichever would be appropriate.
Is there any clever solution for this?
I'm trying to achieve it with a breadth-first search (see wiki)
I also have this toolbox in matlab: http://www.mathworks.com/matlabcentral/fileexchange/4266-grtheory-graph-theory-toolbox but it seems there's no straightforward solution for my problem.
PS. The problem practically is stated as: Transit Network Design Problem: Find such a transport network that minimizes cost of passangers and operators (i.e. optimal subway network for urban area)
Thanks in advance
Rafal
I think the problem as stated in your PS may be a NP problem. If so, there are straightforward solutions only for graphs with very limited numbers of nodes (N ~ <= 20). Other solutions will be approximate, giving rise to only local optimums. The solution to your problem as stated in the question will simply be to calculate all the permutations of the node orders. Again this will become computationally infeasible with comparatively low numbers of nodes (possibly higher than 20 but not much).
Do you need only the shortest paths between all pairs of vertices, or really all paths?