Most classical minimum spanning tree algorithms use the notions of �.docx

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Most classical minimum spanning tree algorithms use the notions of safe and useless edges described in Erickson, but there is an alternative formulation. Let G be a weighted undirected graph, where the edge weights are distinct. We say that an edge e is dangerous if it is the longest edge in some cycle in G, and useful if it does not lie in any cycle in G. Describe and analyze an efficient implementation of the following algorithm, first described by Joseph Kruskal in the same 1956 paper where he proposed Kruskal s algorithm . Examine the edges of G in decreasing order of edge weight; if an edge is dangerous, remove it from G. [Hint: You can solve this problem before we discuss Kruskal s usual algorithm. Also, it won t be as fast as Kruskal s usual algorithm.] 2. Most classical minimum
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