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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.
An animation of generating a 30 by 20 maze using Prim's algorithm. This algorithm is a randomized version of Prim's algorithm. Start with a grid full of walls. Pick a cell, mark it as part of the maze. Add the walls of the cell to the wall list. While there are walls in the list: Pick a random wall from the list.
A* search algorithm; AC-3 algorithm; AKS primality test; Algorithm; Algorithms for calculating variance; All nearest smaller values; Alpha–beta pruning; American flag sort; Apriori algorithm; Automatic differentiation; AVL tree
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 ]
This is how I interpreted the section Prim's algorithm in Introduction to Algorithms (chapter 23, section 2, ISBN 0-262-53196-8). I suggest somebody that can explain this more intuitively edit the article accordingly.
English: Diagram to assist in proof of Prim's algorithm. If Y 1 {\displaystyle Y_{1}} is a minimum spanning tree, and Y is the tree found by Prim's algorithm, we find e , the first edge added by the algorithm which is in Y 1 {\displaystyle Y_{1}} but not in Y.