Viability of smoothed analysis as an explanatory model for simplex performance and worst-case brittleness

Determine whether smoothed analysis of linear programming—specifically the Gaussian perturbation model that independently perturbs all entries of the constraint matrix and right-hand side—provides a viable synthetic model for describing the brittleness of worst-case linear programming instances and, moreover, whether smoothed analysis indeed helps to explain why the simplex method is usually fast on inputs observed in practice, which are typically sparse.

Background

The paper critiques the applicability of smoothed analysis to real-world linear programs, noting that practical and worst-case instances are highly sparse, whereas smoothed analysis perturbs all entries and thereby produces dense data with probability one. This mismatch raises concerns about whether smoothed analysis accurately models either the isolation of worst-case instances or practical performance characteristics.

Within this context, the authors explicitly state that it remains unclear whether smoothed analysis provides a viable synthetic model for worst-case brittleness and whether it helps explain the simplex method’s usual fast performance on practical inputs—thereby formulating an open question about the explanatory scope of smoothed analysis for the simplex method.