In this paper we present a novel approach to NMPC based on state-space partitioning in conjunction with one-step ahead prediction and judicious use of graph theory to deliver an optimized control law which is robust, and is suitable for fast sampling applications. The only on-line computation required is a one-step ahead QP minimization which is linear in the number of inputs. The paper describes the general idea of the method and presents results, whose efficiency is demonstrated by means of a design study.