New class of 0-1 integer programs with tight approximation via linear relaxations

Abstract.

We consider the problem of estimating optima of integer programs { max cx | A x≤b,0≤x≤1, x− integral} where b>0, c≥0 are rational vectors and A is an arbitrary rational m×n matrix. Using randomized rounding we find an efficiently verifiable sufficient condition for optima of such integer programs to be close to the optima q of their linear relaxations. We show that our condition guarantees that for any constant ε>0 and sufficiently large n there exists a feasible integral solution z such that q≥cz≥(1−ε)q.