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

Given a system of constraints ℓ_i ≤ a_i ^T x ≤ u_i, where a_i ∈ {0,1}ⁿ, and ℓ_i, u_i ∈ 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 a_i ∈ {0, 1}ⁿ, a sharp separation in the approximability between the case when L = max{ℓ₁, . . . , ℓ_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 some recently studied pricing problems.