Problem Reduction Graph Model for Discrete Optimization Problems

The paper proposes the problem reduction graph (PRG), an abstract model for discrete optimization problems which uses structural decomposition to reduce problem complexity and constructs the recurrence relations between the problem and its sub problems. We develop several important algorithm patterns for PRG construction, each leading to a special class of concrete problem-solving algorithms in a systematic way. The model supports logical transformation from specifications to algorithmic programs by deductive inference, and thus significantly promotes the automation and reusability of algorithm design.