Consider the following algorithm which decides the Hamiltonian Path problem. For
ID: 3683641 • Letter: C
Question
Consider the following algorithm which decides the Hamiltonian Path problem. For each path in the graph, check if the path connects all vertices. If such a path is found, return True. Otherwise return False after exploring all possible paths. This algorithm runs in linear time in the number of paths and decides the Hamiltonian Cycle problem. Claim: Given that we have a polynomial time algorithm deciding Hamiltonian Cycle, and given that Hamiltonian Cycle is NP-complete, this is sufficient to prove that P = NP. What is correct about this claim's logic and what is incorrect?Explanation / Answer
Answer:) Correct: Hamiltonian Cycle is NP-complete
Incorrect: Given that we have a polynomial time algorithm deciding Hamiltonian Cycle.
There is no known polynomial time algorithm for Hamiltonian Cycle.