At the Leiden Embedded Research Center, we are developing a compiler called Compaan that automatically translates signal processing applications written in Matlab into Kahn Process Networks (KPNs). In general, these signal processing applications are data-flow intensive, requiring large storage capacities, usually represented by matrices. An important issue in Compaan is the derivation of a memory management mechanism that allows for efficient inter-process communication. This mechanism has previously been published and is called the Extended Linearization Model (ELM). The controller needed in the ELM is derived using the Ehrhart theory, leading to a computational intensive procedure. In this paper, we present a new approach to derive the ELM controller, based on the notion of Lexicographically Maximal Preimage. Using polytope manipulations and parametric integer linear programming techniques, we get less computational intensive and easier to be derived controller implementation for the ELM.