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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 ...
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]
If is edge-unweighted every spanning tree possesses the same number of edges and thus the same weight. In the edge-weighted case, the spanning tree, the sum of the weights of the edges of which is lowest among all spanning trees of , is called a minimum spanning tree (MST). It is not necessarily unique.
During his career at Bell Laboratories, Robert Prim along with coworker Joseph Kruskal developed two different algorithms (see greedy algorithm) for finding a minimum spanning tree in a weighted graph, a basic stumbling block in computer network design. His self-named algorithm, Prim's algorithm, was originally discovered in 1930 by ...
The quality of the tree is measured in the same way as in a graph, using the Euclidean distance between pairs of points as the weight for each edge. Thus, for instance, a Euclidean minimum spanning tree is the same as a graph minimum spanning tree in a complete graph with Euclidean edge weights.
By explicitly constructing the complete graph on n vertices, which has n(n-1)/2 edges, a rectilinear minimum spanning tree can be found using existing algorithms for finding a minimum spanning tree. In particular, using Prim's algorithm with an adjacency matrix yields time complexity O(n 2).
A minimum spanning tree (MST) is a minimum-weight, cycle-free subset of a graph's edges such that all nodes are connected. In 2004, Felzenszwalb introduced a segmentation method [4] based on Kruskal's MST algorithm. Edges are considered in increasing order of weight; their endpoint pixels are merged into a region if this doesn't cause a cycle ...
Euclidean minimum spanning tree: algorithms for computing the minimum spanning tree of a set of points in the plane; Longest path problem: find a simple path of maximum length in a given graph; Minimum spanning tree. Borůvka's algorithm; Kruskal's algorithm; Prim's algorithm; Reverse-delete algorithm; Nonblocking minimal spanning switch say ...