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Prim's algorithm. 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 algorithm operates by building this tree ...
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]
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] The key steps of the algorithm are sorting and the use of a disjoint-set ...
The distributed minimum spanning tree (MST) problem involves the construction of a minimum spanning tree by a distributed algorithm, in a network where nodes communicate by message passing. It is radically different from the classical sequential problem, although the most basic approach resembles Borůvka's algorithm.
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).
Parallel algorithms for minimum spanning trees. In graph theory a minimum spanning tree (MST) of a graph with and is a tree subgraph of that contains all of its vertices and is of minimum weight. MSTs are useful and versatile tools utilised in a wide variety of practical and theoretical fields. For example, a company looking to supply multiple ...
However, the single-linkage clustering can be found more efficiently by an alternative algorithm that computes the minimum spanning tree of the input distances using Prim's algorithm, and then sorts the minimum spanning tree edges and uses this sorted list to guide the merger of pairs of clusters.
The reverse-delete algorithm is an algorithm in graph theory used to obtain a minimum spanning tree from a given connected, edge-weighted graph. It first appeared in Kruskal (1956), but it should not be confused with Kruskal's algorithm which appears in the same paper. If the graph is disconnected, this algorithm will find a minimum spanning ...