Boosting and the polynomial approximability of the problem on a minimum affine separating committee

We investigate the intractable problem on a minimum affine separating committee in a space of fixed dimension $n>1$ under the additional constraint that the separated sets are in general position (MASC-GP($n$)). For the investigation of the set of separable subsets that are maximal with respect to inclusion, we apply the game approach, which is traditional for boosting. We construct a polynomial approximate algorithm with guaranteed error estimate $O((m/n\ln m)^{1/2})$, where $m$ is the cardinality of the separated set.