The graph here is without self loops and parallel or anti-parallel edges. In the

Question

The graph here is without self loops and parallel or anti-parallel edges. In the algorithm, always explain their correctness and analyze their complexity. The complexity should be as small as possible. The number of vertices is denoted by n, and the number of edges by m

Consider the following algorithm. Sort the weights in decreasing order. Let these edges be e1, e2, . . . , em so that w(ei) w(ei+1). For j = 1 to m if the removal of ej does not give a disconnected graph, remove ej from the solution. Show by induction that in any stage of this algorithm the graph contains a spanning tree. Deduce that this algorithm finds a minimum spanning tree. NO CODE please.

Explanation / Answer

1. sort the edges into decreasing order of edge weights w.

2. w(ei) >= w(ei+1)

2. T <-- E

3. for each edge e, taken in decreasing order by weight

4. do if T – {e} is a connected graph

5. then T <-- T – {e}

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