Search results
Results from the WOW.Com Content Network
Kruskal's algorithm [1] finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected , it finds a minimum spanning tree . It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle . [ 2 ]
A demo for Prim's algorithm based on Euclidean distance. In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. The ...
Similarly to Prim's algorithm there are components in Kruskal's approach that can not be parallelised in its classical variant. For example, determining whether or not two vertices are in the same subtree is difficult to parallelise, as two union operations might attempt to join the same subtrees at the same time.
For example, Kruskal's algorithm processes edges in turn, deciding whether to include the edge in the MST based on whether it would form a cycle with all previously chosen edges. Both Prim's algorithm and Kruskal's algorithm require processes to know the state of the whole graph, which is very difficult to discover in the message-passing model.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
Examples of such greedy algorithms are Kruskal's algorithm and Prim's algorithm for finding minimum spanning trees and the algorithm for finding optimum Huffman trees. Greedy algorithms appear in the network routing as well. Using greedy routing, a message is forwarded to the neighbouring node which is "closest" to the destination.
All the above algorithms have biases of various sorts: depth-first search is biased toward long corridors, while Kruskal's/Prim's algorithms are biased toward many short dead ends. Wilson's algorithm, [1] on the other hand, generates an unbiased sample from the uniform distribution over all mazes, using loop-erased random walks.
It is the reverse of Kruskal's algorithm, which is another greedy algorithm to find a minimum spanning tree. Kruskal’s algorithm starts with an empty graph and adds edges while the Reverse-Delete algorithm starts with the original graph and deletes edges from it. The algorithm works as follows: Start with graph G, which contains a list of ...