Question

2. Show how to efficiently solve the vertex cover problem for the special case where the network is a tree, and all vertices have weight 1 (so you want to select the smallest set of vertices that touches each edge). Figure 1: The network at left has 7 edges, and we can decompose this edge set into the 4 colored pairs shown at right.

          2. Show how to efficiently solve the vertex cover problem for the special case
where the network is a tree, and all vertices have weight 1 (so you want
to select the smallest set of vertices that touches each edge).
Figure 1: The network at left has 7 edges, and we can decompose this edge set
into the 4 colored pairs shown at right.

2. Show how to efficiently solve the vertex cover problem for the special case
where the network is a tree, and all vertices have weight 1 (so you want
to select the smallest set of vertices that touches each edge).
Figure 1: The network at left has 7 edges, and we can decompose this edge set
into the 4 colored pairs shown at right.

Added by Emilio F.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

09/10/2022

Step 1

Since all vertices have weight 1, it is optimal to choose the leaves of the tree in the vertex cover set. This is because each leaf is connected to only one edge, so selecting a leaf will cover that edge. Show more…

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Show how to efficiently solve the vertex cover problem for the special case where the network is a tree, and all vertices have weight 1 (so you want to select the smallest set of vertices that touches each edge). Figure 1: The network at left has 7 edges, and we can decompose this edge set into the 4 colored pairs shown at right. 2. Show how to efficiently solve the vertex cover problem for the special case where the network is a tree, and all vertices have weight 1 (so you want to select the smallest set of vertices that touches each edge) Figure 1: The network at left has 7 edges, and we can decompose this edge set into the 4 colored pairs shown at right