Provide the pseudocode of a greedy distributed minimal weighted connected ver$-$

tex cover based algorithm using the algorithm described in Sect. $13\mathrm{.}3\mathrm{.}2.$ Work out

its time and message complexities. Also, show the operation of this algorithm step$-$

by$-$step in the example graph of Fig. $13\mathrm{.}14$ where each vertex is labeled by its

weight.

Provide the DFS tree of the graph of Fig. $13\mathrm{.}14$ starting from the vertex with the

heaviest weight. Show that all nonleaf nodes of this tree constitute a vertex cover.