  In this paper, we present an analysis of the strength of sparse
cutting-planes for mixed integer linear programs (MILP) with sparse
formulations. We examine three kinds of problems: packing problems, covering
problems, and more general MILPs with the only assumption that the objective
function is non-negative. Given a MILP instance of one of these three types,
assume that we decide on the support of cutting-planes to be used and the
strongest inequalities on these supports are added to the linear programming
relaxation. Call the optimal objective function value of the linear programming
relaxation together with these cuts as $z^{cut}$. We present bounds on the
ratio of $z^{cut}$ and the optimal objective function value of the MILP that
depends only on the sparsity structure of the constraint matrix and the support
of sparse cuts selected, that is, these bounds are completely data independent.
These results also shed light on the strength of scenario-specific cuts for two
stage stochastic MILPs.
