graph-theory

What is the most efficient way to generate a large (~ 300k vertices) random planar graph ("random" here means uniformly distributed)? Another possibility consists in randomly choosing coordinates and then compute a Delaunay Triangulation, which is a planar graph (and looks nice as well). See http://en.wikipedia.org/wiki/Delaunay_triangulation There are O(n log(n)) algorithms to compute such a triangulation. Without any other requirements, I'd say look up random maze generation. If you want cycles in the graph, remove some walls at random from a simple maze. The intersections in the maze become

I quote from Artificial Intelligence: A Modern Approach : The properties of depth-first search depend strongly on whether the graph-search or tree-search version is used. The graph-search version, which avoids repeated states and redundant paths, is complete in finite state spaces because it will eventually expand every node. The tree-search version, on the other hand, is not complete [...]. Depth-first tree search can be modified at no extra memory cost so that it checks new states against those on the path from the root to the current node; this avoids infinite loops in finite state spaces

I need to use the connected component labeling algorithm on an image in a C++ application. I can implement that myself, but I was trying to use Boost's union-find/disjoint sets implementation since it was mentioned in the union-find wiki article. I can't figure out how to create the disjoint_sets object so that it'll work with the image data I have (unsigned shorts). What am I missing? The examples in the Boost documentation aren't making any sense to me. Do I need all the extra Graph mumbo-jumbo in those examples when I have an image? OR, is there already an OpenCV connected component

There is a custom implementation of KSPA which needs to be re-written. The current implementation uses a modified Dijkstra's algorithm whose pseudocode is roughly explained below. It is commonly known as KSPA using edge-deletion strategy i think so. (i am a novice in graph-theory). Step:-1. Calculate the shortest path between any given pair of nodes using the Dijkstra algorithm. k = 0 here. Step:-2. Set k = 1 Step:-3. Extract all the edges from all the ‘k-1’ shortest path trees. Add the same to a linked list Edge_List. Step:-4. Create a combination of ‘k’ edges from Edge_List to be deleted at

I want to create a plot showing connections between nodes from an adjacency matrix like the one below. gplot seems like the best tool for this. However, in order to use it, I need to pass the coordinate of each node. The problem is that I don't know where the coordinates should be, I was hoping the function would be capable of figuring out a good layout for me. For example here's my output using the following arbitrary coordinates: A = [1 1 0 0 1 0; 1 0 1 0 1 0; 0 1 0 1 0 0; 0 0 1 0 1 1; 1 1 0 1 0 0; 0 0 0 1 0 0]; crd = [0 1; 1 1; 2 1; 0 2; 1 2; 2 2]; gplot (A, crd, "o-"); Which is hard to