On the approximability of the maximum feasible subsystem problem with 0/1-coefficients

Given a system of constraints `i ≤ ai x ≤ ui, where ai ∈ {0, 1}, and `i, ui ∈ R+, for i = 1, . . . ,m, we consider the problem Mrfs of finding the largest subsystem for which there exists a feasible solution x ≥ 0. We present approximation algorithms and inapproximability results for this problem, and study some important special cases. Our main contributions are : 1. In the general case, where ai ∈ {0, 1}, a sharp separation in the approximability between the case when L = max{`1, · · · , `m} is bounded above by a polynomial in n and m, and the case when it is not. 2. In the case where A is an interval matrix, a sharp separation in approximability between the case where we allow a violation of the upper bounds by at most a (1+ ) factor, for any fixed > 0 and the case where no violations are allowed. Along the way, we prove that the induced matching problem on bipartite graphs is inapproximable beyond a factor of Ω(n 1 3− ), for any > 0 unless NP=ZPP. Finally, we also show applications of Mrfs to the recently studied pricing problems.