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On the complexity of approximating the independent set problem
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Journal of the ACM (JACM)
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MIN PB is the class of minimization problems whose objective functions are bounded by a polynomial in the size of the input. We show that there exist several problems that are MIN PB-complete with respect to an approximation preserving reduction. These problems are very hard to approximate; in polynomial time they cannot be approximated within nε for some ε 0, where n is the size of the input, provided that P ≠ NP. In particular, the problem of finding the minimum independent dominating set in a graph, the problem of satisfying a 3-SAT formula setting the least number of variables to one, and the minimum bounded 0 - 1 programming problem are shown to be MIN PB-complete.We also present a new type of approximation preserving reduction that is designed for problems whose approximability is expressed as a function of some size parameter. Using this reduction we obtain good lower bounds on the approximability of the treated problems.