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Constraint Theory 

Multidimensional Mathematical Model Management Series: 

Ifsr International Series on Systems Science and Engineering, Vol. 23 Friedman, George 2005, Approx. 200 p., Hardcover ISBN: 0-387-23418-7

Available from Springer Academic Publishers - click here for more

About this book

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.

Written for: Engineers and mathematicians who construct math models and the managers who fund and employ these models.

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Read sample pages here!

Praise for Dr. Friedman's book on Constraint Theory:

"In this book, George Friedman demonstrates that, with high probability, large mathematical models of physical systems are defective. Rather than using defective models in striving to gain insight into a physical system, Friedman demonstrates how to use the bipartite graph of the defective model to gain an understanding of where the model is inconsistent, in order to overcome that inconsistency. Then, rather than subjecting the unsuspecting modeler to a never-ending effort to compute that which the model is incapable of computing, Friedman demonstrates how to use the bipartite graph to determine whether a proposed computation is allowable. By spending a relatively modest amount of time in gaining insight on the model itself, the modeler may save large amounts of time that would otherwise be wasted in striving to gain insight about a system with a model that is unsuited to that purpose.

Friedman's accomplishment represents engineering at its finest. The choice of subject matter must be honored by the experience gained in his many years of high-level service in the company now known as Northrop-Grumman. The credibility of the theory rests upon the formal proofs which are interspersed among the illuminating hypothetical dialog sequences between manager and analyst, which bring out distinctions that the organization must face, en route to accepting Friedman's work as essential to achieve quality control in developing and applying large models."

- Dr. John Warfield

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Last modified: April 05, 2005