Using Aweighted Graph Of A Graph

1367 WordsMay 15, 20166 Pages
INTRODUCTION- we define a graph as a collection of a number of vertices and edges, and each of its edge basically connects a pair of its vertices. Whereas a tree can be defined as an acyclic graph that is connected. The edges of a graph are assigned with some numerical valuethat may represent the distance between the vertices, the cost or the time etc. that is why it is called aweighted graph. An acyclicgraph that is weightedis known as a weighted tree. The minimum spanning tree (MST) in a weighted graph is called aspanning tree. In this graph the sum of the weights of all the edges is minimum. Multiple MST are present in a graph, but all of theseneedto have unique sum total cost.The problem in constructing MST in an undirected, connected, weighted graph is one of the most known classic optimization problems.Such problems can be solved by greedy or dynamic algorithms within polynomial time.In 1926, first practical problem related to the MST was identified by Boruvka. But now, there are several practically relatedalternatives of the MST problem that were verified to belong to the NP-hard class. For an instance the Degree-Constrained MST problem [2],Bounded Diameter MST (BDMST) problem framed by the researchers named: Nghia and Binh [2], and the Capacitated Minimum SpanningTree problem [2]. Another one called the deterministic MST problem has also been well calculated and many effective algorithms have beenintroduced by many researchers. However, the Kruskal’s algorithm and

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