Strong Lower Bounds on the Approximability of some NPO PB-Complete Maximization Problems
نویسنده
چکیده
The approximability of several NP maximization problems is investigated and strong lower bounds for the studied problems are proved. For some of the problems the bounds are the best that can be achieved, unless P = NP. For example we investigate the approximability of Max PB 0 ? 1 Programming, the problem of nding a binary vector x that satisses a set of linear relations such that the objective value P c i x i is maximized, where c i are binary numbers. We show that, unless P = NP, Max PB 0 ? 1 Programming is not approximable within the factor n 1?" for any " > 0, where n is the number of inequalities, and is not approximable within m 1=2?" for any " > 0, where m is the number of variables. Similar hardness results are shown for other problems on binary linear systems, some problems on the satissability of boolean formulas and the longest induced cycle problem.
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