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http://dx.doi.org/10.7236/JIWIT.2011.11.5.159

A Minimum Spanning Tree Algorithm for Directed Graph  

Choi, Myeong-Bok (강릉원주대학교 멀티미디어공학과)
Lee, Sang-Un (강릉원주대학교 멀티미디어공학과)
Publication Information
The Journal of the Institute of Internet, Broadcasting and Communication / v.11, no.5, 2011 , pp. 159-171 More about this Journal
Abstract
This paper suggests an algorithm that obtains the Minimum Spanning Tree for directed graph (DMST). The existing Chu-Liu/Edmonds DMST algorithm has chances of the algorithm not being able to find DMST or of the sum of ST not being the least. The suggested algorithm is made in such a way that it always finds DMST, rectifying the disadvantage of Chu-Liu/Edmonds DMST algorithm. Firstly, it chooses the Minimum-Weight Arc (MWA) from all the nodes including a root node, and gets rid of the nodes in which cycle occurs after sorting them in an ascending order. In this process, Minimum Spanning Forest (MST) is obtained. If there is only one MSF, DMST is obtained. And if there are more than 2 MSFs, to determine MWA among all MST nodes, it chooses a method of directly calculating the sum of all the weights, and hence simplifies the emendation process for solving a cycle problem of Chu-Liu/Edmonds DMST algorithm. The suggested Sulee DMST algorithm can always obtain DMST that minimizes the weight of the arcs no matter if the root node is set or not, and it is also capable to find the root node of a graph with minimized weight.
Keywords
Directed Graph; Minimum Spanning Tree; Directed Graph Minimum Spanning Tree Cycle; Minimum Spanning Forest;
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