graph-algorithm

I am referring to Skienna's Book on Algorithms. The problem of testing whether a graph G contains a Hamiltonian path is NP-hard , where a Hamiltonian path P is a path that visits each vertex exactly once. There does not have to be an edge in G from the ending vertex to the starting vertex of P , unlike in the Hamiltonian cycle problem. Given a directed acyclic graph G ( DAG ), give an O(n + m) time algorithm to test whether or not it contains a Hamiltonian path. My approach, I am planning to use DFS and Topological sorting . But I didn't know how to connect the two concepts in solving the

I know Prim's algorithm and I know its implementation but always I skip a part that I want to ask now. It was written that Prim's algorithm implementation with Fibonacci heap is O(E + V log(V)) and my question is: what is a Fibonacci heap in brief? How is it implemented? And How can you implement Prim's algorithm with a Fibonacci heap? A Fibonacci heap is a fairly complex priority queue that has excellent amoritzed asymptotic behavior on all its operations - insertion, find-min, and decrease-key all run in O(1) amortized time, while delete and extract-min run in amortized O(lg n) time. If you

I have a matrix with values 0 or 1 and I would like to obtain a list of groups of adjacent 1's. For example, the matrix mat = rbind(c(1,0,0,0,0), c(1,0,0,1,0), c(0,0,1,0,0), c(0,0,0,0,0), c(1,1,1,1,1)) > mat [,1] [,2] [,3] [,4] [,5] [1,] 1 0 0 0 0 [2,] 1 0 0 1 0 [3,] 0 0 1 0 0 [4,] 0 0 0 0 0 [5,] 1 1 1 1 1 should return the following 4 connected components: C1 = {(1,1);(2,1)} C2 = {(2,4)} C3 = {(3,3)} C4 = {(5,1);(5,2);(5,3);(5,4);(5,5)} Does anybody has an idea of how to do it fast in R? My real matrix is indeed rather large, like 2000x2000 (but I expect that the number of connected

Topological sort can be done using both a DFS(having edges reversed) and also using a queue . A BFS can also be done using a queue . Is there any relationship between the way elements are stored and retrieved while using queue for a BFS to that when used a queue for topological sorting . Clarification will be helpful . Thanks. No, there is not necessarily any relationship. I assume you are referring to the algorithm by Kahn from wikipedia/Topological_sorting#Algorithms , which wikipedia notes: Note that, reflecting the non-uniqueness of the resulting sort, the structure S can be simply a set

I'm developing an image warping iOS app with OpenGL ES 2.0. I have a good grasp on the setup, the pipeline, etc., and am now moving along to the math. Since my experience with image warping is nil, I'm reaching out for some algorithm suggestions. Currently, I'm setting the initial vertices at points in a grid type fashion, which equally divide the image into squares. Then, I place an additional vertex in the middle of each of those squares. When I draw the indices, each square contains four triangles in the shape of an X. See the image below: After playing with photoshop a little, I noticed