0/1-integer programming: Optimization and augmentation are equivalent

Abstract

For every family of sets F ⊆ {0, 1}n the following problems are strongly polynomial time equivalent: given a feasible point x0 ϵ F and a linear objective function c ϵ ℤn, find a feasible point x* ϵ F that maximizes cx (Optimization), _9 find a feasible point xnew ϵ F with cxnew > cx0 (Augmentation), and find a feasible point xnew ϵ F with c xnew > c x0 such that xnew—x0is “irreducible” (Irreducible Augmentation). This generalizes results and techniques that are well known for 0/1- integer programming problems that arise from various classes of combinatorial optimization problems.