ICALP 1993: Automata, Languages and Programming pp 52-63 | Cite as
Polynomially bounded minimization problems which are hard to approximate
Abstract
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 which 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 in some size parameter. Using this reduction we obtain good lower bounds on the approximability of the treated problems.
Keywords
Turing Machine Short Computation Input Instance 3CNF Formula Linear ReductionPreview
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