CPSC 411: Quiz 11
November 13, 2008

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  1. (2 pts) Suppose you know that the Hamiltonian cycle problem (HC) is NP-complete and you need to prove that the vertex cover problem (VC) is NP-complete. You need to show that there is a reduction from one of these problems to the other. Which way should the reduction go: given any HC input, construct a VC input, OR given any VC input, construct a HC input?





  2. (2 pts) Suppose f is a polynomial reduction from the traveling salesman problem (TSP) to the 3SAT problem. So given a TSP input x, f produces a 3SAT input f(x). Which of the following relationships must hold between x and f(x)? Choose one.



  3. (1 pts) True or False: Suppose we know that there is a polynomial reduction from problem P1 to problem P2. If there is a polynomial-time algorithm for P1, then there is a polynomial-time algorithm for P2.