Comparative Analysis of the Kruskal and Boruvka Algorithms in Solving Minimum Spanning Tree on Complete Graph

Abstract

The problem that is often encountered in daily life is connecting all points in one work domain with a low optimization value, for example, the most economical cost required to connect a water pipe to each house in an area. To solve this problem, a system that can find a path that connects all points in one work domain with the lowest optimization is needed. In this study, the system was built using two algorithms, namely, Kruskal and Boruvka algorithms, and a complete graph is used as a modeling of the problem. Using these two algorithms, the system will find the optimum path that connects all points in the complete graph; then, the system also displays a comparison between the two algorithms in finding the optimum route. The data used is dynamic, meaning the users can enter and change the value of the side of the complete graph as needed. From the tests that have been done, it is found that the Kruskal algorithm is more effective than the Boruvka to find the minimum spanning tree in a complete graph with some nodes, and sides are 15 points and 105 sides.