最小全域木問題とPrimのアルゴリズムに関する論文
令和8年1月8日|p.19
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## 1. Introduction
The purpose of this paper is to study the problem of finding a minimum spanning tree in a graph.
A minimum spanning tree (MST) 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.
There are several algorithms for finding an MST, including Prim's algorithm, Kruskal's algorithm, and Borůvka's algorithm.
In this paper, we will focus on Prim's algorithm and its implementation details.
Prim's algorithm starts from an arbitrary vertex and grows the MST one edge at a time by adding the smallest edge that connects a vertex in the MST to a vertex outside the MST.
We will also discuss the time complexity of Prim's algorithm and compare it with other MST algorithms.