New integer linear programming formulation for the scheduling problem in data path synthesis

Abstract

A novel approach is presented to the operation scheduling problem in data path synthesis. After obtaining the start time and the require time of each operation by the ASAP (as soon as possible) and ALAP (as late as possible) methods, respectively, an integer linear programming (ILP) formulation is formed to solve the scheduling problem. The objective is to fully utilize the hardware resources, i.e., to minimize the requirement of function units under a given timing constraint. The formulation can be generalized to support multicycle operations, multiple operations per cycle, pipelined data paths, mutually exclusive operations, and variables' lifetime consideration in a data path. A fifth-order filter containing 26 addition and 8 multiplication operations can be scheduled optimally for the cases from 17 cycles to 21 cycles per minute on a VAX-11/8800.