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]

2025年2月28日 · A minimum spanning tree (MST) is a tree-like subgraph of a connected, undirected graph that includes all vertices and has the minimum possible total edge weight among all spanning trees.

我们定义无向连通图的 最小生成树（Minimum Spanning Tree，MST）为边权和最小的生成树。 注意：只有连通图才有生成树，而对于非连通图，只存在生成森林。 Kruskal 算法. Kruskal 算法是一种常见并且好写的最小生成树算法，由 Kruskal 发明。

2025年3月5日 · Kruskal's algorithm efficiently finds the minimum spanning tree of a weighted, connected, and undirected graph by sorting edges and adding them to the tree while avoiding cycles, utilizing a disjoint set data structure for cycle detection.

2025年2月26日 · Prim’s algorithm is guaranteed to find the MST in a connected, weighted graph. It has a time complexity of O ( (E+V)*log (V)) using a binary heap or Fibonacci heap, where E is the number of edges and V is the number of vertices. It is a relatively simple algorithm to understand and implement compared to some other MST algorithms. Disadvantages:

2016年2月23日 · 本篇文章旨在介紹Graph中常見的應用：Minimum Spanning Tree(MST，最小生成樹)。 在介紹演算法時，繼續會用上Set(集合)的概念，如果對Set有基本概念，相信讀者一定可以躺著讀完這篇。

2025年1月10日 · A minimum spanning tree (MST) of an edge-weighted graph is a spanning tree whose weight (the sum of the weights of its edges) is no larger than the weight of any other spanning tree. Assumptions. To streamline the presentation, we adopt the following conventions: The graph is connected.

The MST problem is a standard graph (and also optimization) problem defined as follows: Given a connected undirected weighted graph G = (V, E), select a subset of edges of G such that the graph is still connected but with minimum total weight.

2016年12月29日 · 一个连通图的生成树是图的极小联通子图，它包含图中所有顶点，并且只含尽可能少的边。 这意味着对于生成树来说，若砍去一条边，就会使生成树变成非连通图；若增加一条边，就会形成图中的一条回路。 对于一个带权连通 无向图 G= (V,E)，生成树不同，每棵树的权（即树中所有边上的权值之和）也可能不同。 社R为G的所有生成树的集合，若T为R中权值之和最小的那棵生成树，则T成为G的最小生成树。 构造最小生成树有多种算法，但大多数算法是利用了 …

Minimum Spanning Tree (MST) is a fundamental concept in graph theory and algorithms. Given a connected, weighted graph, an MST is a spanning tree (a subset of the edges that keeps the graph connected without any cycles) that has the minimum possible total edge weight.