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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 ...
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]
Greedy algorithms fail to produce the optimal solution for many other problems and may even produce the unique worst possible solution. One example is the travelling salesman problem mentioned above: for each number of cities, there is an assignment of distances between the cities for which the nearest-neighbour heuristic produces the unique ...
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.
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.
The article currently claims "However, for graphs that are sufficiently dense, Prim's algorithm can be made to run in linear time, meeting or improving the time bounds for other algorithms.[10]". The reference is to Tarjan, "Data Structures and Network Algorithms", page 77.
Within Prim's algorithm, each successive minimum spanning tree edge can be found by a sequential search through an unsorted list of the smallest edges connecting the partially constructed tree to each additional vertex. This choice saves the time that the algorithm would otherwise spend adjusting the weights of vertices in its priority queue.