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Consider the so - called k - Minimum Spanning Tree ( k - MST ) problem, which is defined as follows. An instance of the
Consider the socalled Minimum Spanning Tree MST problem, which is defined as follows.
An instance of the MST problem is given by a connected undirected graph with edge weights : and a natural number The question is to find a tree with exactly nodes that is a subgraph of and minimises the weight among all such trees. Informally, MST is the variant of the minimum spanning tree problem, where instead of a spanning tree one wants to find a tree with exactly nodes.
What would be the result if we apply Prim's, respectively Kruskal's, algorithm to the problem by stopping both algorithms after edges have been added? In the following we refer to these versions of Prim's and Kruskal's algorithm as the modified algorithm of Prime or Kruskal, respectively.
Q Modified algorithm of Kruskal
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Consider the following graph.
For which of the following edge weights, assigned to the graph above, does the modified algorithm of Kruskal provide a wrong result assuming that hick all answers for which this is the case.
Here, means that the edge between vertices a and has weight
onsider the tollowing graph.
For which of the following edge weights, assigned to the graph above, and starting vertex does the modified algorithm of Prim provide a wrong result assuming that Tick all correct answers.
Here, means that the edge between vertices a and has weight and a means that the start vertex for the modified alqorithm of Prim is set to the vertex
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