Constraint Theory: Multidimensional Mathematical Model Management

The enormous potential of digital computation to manage new complex systems is impeded by exponential increases in complexity. As the model's dimensionality increases from hundreds to thousands of variables, and as submodels constructed by diverse technical teams are integrated into the total model, the model is likely to become inconsistent and even more likely, the computational requests on the model become unallowable. This text analyzes the way constraint theory employs bipartite graphs and constraint matrices to detect and correct these well-posed problems. It also presents the process of locating the "kernel of constraint," literally trillions of times faster than a random search, determining consistency and compatibility within seconds. This text is an invaluable reference to all engineers, mathematicians and managers concerned with modeling.