Problem 7 (20 points): Consider the network topology of Figure 2. Compute the minimum-cost spanning tree using the following two algorithms. For every algorithm iteration, show the nodes that are already selected as part of the tree and the edges that connect them (a) Kruskals Algorithm i. Step 1: Initially, remove all the edges in the network graph and put them in a set S. Every node is considered as a root of an empty sub-tree. 15 12 Figure 2: The Network Topology and associated edge costs in Problem 7 ii. Step 2: Add a minimum-weight outgoing edge from set S back to the graph, which extends an existing sub-tree by one node (make sure there is no cycle). iii. Step 3: Repeat step 2 until all the sub-trees are connected to be a spanning tree. (b) Prim-Dijkstras Algorithm i. Step 1: Select a starting node at random. ii. Step 2: Add a minimum-weight outgoing edge (an edge that does not belong to the current tree) that extends the tree by one node. iii. Repeat until all nodes of the network are spanned