)This problem will explore how different algorithms play out with the same weighted graph. a) Use the nearest neighbor algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex E, and find the weight of this circuit. b) Use the greedy algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex E, and find the weight of this circuit. Also, write down the edges in the order that you choose them when constructing the circuit as you apply the Greedy Algorithm. c) It turns out that neither the nearest neighbor algorithm nor the greedy algorithm gives a Hamiltonian circuit of minimum total weight starting at vertex E. Find some Hamiltonian circuit starting at vertex E of total weight smaller than those of the circuits you found in parts (a) and (b).
1)This problem will explore how different algorithms play out with the same weighted graph.
a) Use the nearest neighbor algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex E, and find the weight of this circuit.
b) Use the greedy algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex E, and find the weight of this circuit. Also, write down the edges in the order that you choose them when constructing the circuit as you apply the Greedy Algorithm.
c) It turns out that neither the nearest neighbor algorithm nor the greedy algorithm gives a Hamiltonian circuit of minimum total weight starting at vertex E. Find some Hamiltonian circuit starting at vertex E of total weight smaller than those of the circuits you found in parts (a) and (b).
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