University of Delaware Algorithms and Data Structures Questionnaire

Question Description

I’m working on a algorithms & data structures question and need an explanation and answer to help me learn.

For each of the statements below, determine whether it is True or False. Please briefly explain your
answer or provide a counterexample for each of them.

(1) If Y ∈ NP-COMPLETE, X ∈ NP, and X ≤P Y, then X in NP-COMPLETE.

(2) Is it possible that P = NP and NP = EXP?

(3) Is it possible that both NP = PSPACE?

(4) For some NP-hard problems, a constant approximation solution is not possible.

(5) For some NP-hard problems, they can be approximated arbitrarily close to the optimum.

(6) The relationship between maximum independent set and minimum vertex cover is like the
relationship between maximum flow and minimum cut.

(7) In a tournament, there always exists one or more Hamiltonian paths. In such a path, each
player always beats its immediate successor.

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