Near-Optimal Nonapproximability Results for Some NPO PB-Complete Problems

We show that a number of Npo PB-complete problems, including Min Ones and Max Ones, are hard to approximate within n 1\Gammaffl for arbitrary ffl ? 0. Keywords: Approximation, Computational complexity, Combinatorial problems. 1 Introduction Npo PB is the class of NP optimization problems whose objective function is bounded by some polynomial in the size of the input. It is well-known that many problems that are complete for Npo PB are notoriously hard to approximate and near-optimal lower bounds on the approximability of Npo PB-complete problems such as Min # Sat and Min PB 0-1 Programming have appeared in the literature [5]. However, there are still many problems for which tight bounds are not known. In this paper we provide such bounds for five Npo PB-complete problems: Min Ones, Min Dones, Max Ones, Max Dones and Max PB 0/1 Programming. For each of these problems we show that they cannot be approximated within n 1\Gammaffl for any ffl ? 0 where n is the number of variables. S..