3. Consider a complete weighted graph with 512 vertices. (a) Which of the following will closely represent the worst cost (in

3. Consider a complete weighted graph with 512 vertices. (a) Which of the following will closely represent the worst cost (in number of operations) required to build the graph’s Minimum Spanning Tree (MST) using Kruskals algorithm: (1) 213 (2) 216 (3) 220 (b) A faster algorithm to do the above task is to divide the adjacency matrix into equal submatrices and assign each to a processor to compute the MST for the corresponding subgraph in parallel with the other processors. After that, we combine the sub-trees into one MST. If we have 256 such processors, and the combine cost is negligible, which of the following will closely represent the worst cost (in number of operations) required to build the total graph’s MST: (1) 211 (2) 213 (3) 216 Important: in both (a) and (b) give the reasons for your choice.



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