Provide short answers to the following questions: (a) Suppose we know that a problem X is NP-complete. Suppose we discover a polynomialtime algorithm for X. Would that imply that the SATISFIABILITY problem can besolved in polynomial time? Explain your answer. (b) Suppose we know that a problem X belongs to the class NP. Suppose we discover thatthere is a polynomial time algorithm for X. Would that imply that the SATISFIABIL-ITY problem can be solved in polynomial time? Explain your answer. (c) Suppose we discover an O(n3) algorithm for SATISFIABILITY. Would that imply thatevery problem in NP can be solved in O(n3) time? Why or why not?
Provide short answers to the following questions: (a) Suppose we know that a problem X is NP-complete. Suppose we discover a polynomialtime algorithm for X. Would that imply that the SATISFIABILITY problem can besolved in polynomial time? Explain your answer. (b) Suppose we know that a problem X belongs to the class NP. Suppose we discover thatthere is a polynomial time algorithm for X. Would that imply that the SATISFIABIL-ITY problem can be solved in polynomial time? Explain your answer. (c) Suppose we discover an O(n3) algorithm for SATISFIABILITY. Would that imply thatevery problem in NP can be solved in O(n3) time? Why or why not?
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Provide short answers to the following questions:
(a) Suppose we know that a problem X is NP-complete. Suppose we discover a polynomial
time algorithm for X. Would that imply that the SATISFIABILITY problem can be
solved in polynomial time? Explain your answer.
(b) Suppose we know that a problem X belongs to the class NP. Suppose we discover that
there is a polynomial time algorithm for X. Would that imply that the SATISFIABIL-
ITY problem can be solved in polynomial time? Explain your answer.
(c) Suppose we discover an O(n3) algorithm for SATISFIABILITY. Would that imply that
every problem in NP can be solved in O(n3) time? Why or why not?
every problem in NP can be solved in O(n3) time? Why or why not?
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