1. Let G be a graph with n vertices and m edges such that all the edge weights in G are integers in the range [1,n]. Give an algorithm for finding a minimum spanning tree for G in O(mlog∗ n) time.2. Consider a diagram of a telephone network, which is a graph G whose vertices represent switching centers, and whose edges represent communication lines joining pairs of centers. Edges are marked by their bandwidth, and the bandwidth of a path is equal to the lowest bandwidth among the path’s edges. Give an algorithm that, given a network and two switching centers a and b, outputs the maximum bandwidth of a path between a and b.
1. Let G be a graph with n vertices and m edges such that all the edge weights in G are integers…
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