Given a 4-cube with faulty nodes {0001, 0011, 1000, 1010, 1111},

• Determine the safety level of each node.

• Prove that if the source node is safe, then there is a healthy Hamiltonian path from the source to any destination in any cube. (Hint: Use induction based on the distance between the source and destination nodes).

• Show how to route a message from node 1110 to node 0000 using safety levels.

• Provide a ring routing algorithm using two virtual networks.