Optimizing the minimum spanning tree (MST) and its relationship with the minimum cut

Abstract

The ST ST is a sub-tree of the original network so that the network graph can contain more than one sub-tree that reaches all the vertices of the network and the minimum spanning tree MST is the smallest measure among all the weights of the sub-spanning trees. To get the MST in a simplified way the Kruskal algorithm and the prime algorithm have been applied to several examples. In this work, we applied the new technique to the same examples, and the results were equal or have less value comparing with the above algorithms. The main idea of this technique is to link between the subject of the MST and the subject of the minimum cutoff, so that all the paths of the original graph were extracted and we calculated the weight of each path and chose the path that carried the largest weight, then we can grade by taking the paths according to need from largest to smallest and we cut the edge with the largest weight from that path and continue this process until the conditions of the ST are met.