Approximating linear programming is log-space complete for P

Abstract

We consider here two approximations of the general linear programming problem. A solution approximation requires a vector close to an optimal vector solution in some suitable norm. A value approximation seeks for a vector at which the objective function attains a value near to the optimum. We show that approximating within any factor ϵ > 0 any of those problems is P-complete under log-space reductions. In order to show the above result we prove the nonparallel approximability of computing the number of true gates in a Boolean circuit.