## The approximability of satisfying subsystems of linear systems

We study the computational complexity of the problem which consists, given a system of linear relations, of finding a solution satisfying as many relations as possible. This general combinatorial problem, referred to as maxfls, is considered for the four basic types of relations =, {ge}, > and {ne}. The problem can also be seen as a minimization problem, minulr, where we want to find a solution violating as few relations as possible. The problem is NP-hard for =, {ge} or > relations, even when restricted to homogeneous systems with bipolar coefficients, whereas it is trivial for {ne} relations. In thismore »