You are given an undirected graph G = (V, E) with positive weights on the edges....
You are given an undirected graph G = (V, E) with positive weights on the edges. If the edge weights are distinct, then there is only one MST, so both Prim’s and Kruskal’s algorithms will find the same MST. If some of the edge weights are the same, then there can be several MSTs and the two algorithms could find different MSTs. Describe a method that forces Prim’s algorithm to find the same MST of G that Kruskal’s algorithm finds.
Homework Answers
Let us Consider the following undirected Graph G
a) Prim’s algorithm :
b) Kruskal’s algorithm :
If we observe the MST's of both Prim’s and Kruskal’s algorithms for given undirected graph G
both are finds the same MST's.
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This problem is dealing with Discrete Math. Please answer fully
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the answer.
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This problem is dealing with Discrete Math. Please answer fully
and clearly, and show/explain all steps or proofs that you state in
the answer.
4. Let (G, w) be a connected graph with weights on edges so that all weights are distinct positive real numbers. Suppose we find a MST (minimum spanning trees ) in G by using Prim's algorithm. Prove that no matter what vertex we begin with in Prim algorithm, the set of all weights on edges in...
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