A fully polynomial epsilon approximation cutting plane algorithm for solving combinatorial linear programs containing a sufficiently large ball

A cutting plane algorithm is presented for finding ϵ-appropriate solutions to integer programs contained in the unit hypercube and represented by a separation oracle. Under the assumption that a polynomially bounded ball is contained in the feasible region of the problem, it is demonstrated that the algorithm is an oracle fully polynomial ϵ approximation scheme. Implications of the result for 0/1 integer programming are discussed.