The.Algorithm.Design.Manual.Springer-Verlag.1998

Modeling the Problem
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Modeling the Problem
Modeling is the art of formulating your application in terms of precisely described, well-understood
problems. Proper modeling is the key to applying algorithmic design techniques to any real-world
problem. Indeed, proper modeling can eliminate the need to design or even implement algorithms by
relating your application to what has been done before. Proper modeling is the key to effectively using
the problem catalog in Part II of this book.
Real-world applications involve real-world objects. You might be working on a system to route traffic in
a network, to find the best way to schedule classrooms in a university, or to search for patterns in a
corporate database. Most algorithms, however, are designed to work on rigorously defined abstract
structures such as permutations, graphs, and sets. After all, if you can't define what you want to do, you
can't hope to compute it. You must first describe your problem abstractly, in terms of fundamental
structures and properties.
Whatever your application is, odds are very good that others before you have stumbled upon the same
algorithmic problem, perhaps in substantially different contexts. Therefore, to find out what is known
about your particular ``widget optimization problem,'' you can't hope to look in a book under widget. You
have to formulate widget optimization in terms of computing properties of abstract structures such as:
● Permutations, which are arrangements, or orderings, of items. For example, and
are two distinct permutations of the same set of four integers. Permutations are likely
the object in question whenever your problem seeks an ``arrangement,'' ``tour,'' ``ordering,'', or
``sequence.''
● Subsets, which represent selections from a set of items. For example, and are two
distinct subsets of the first four integers. Order does not matter in subsets the way it does with
permutations, so the subsets and would be considered identical. Subsets are likely
the object in question whenever your problem seeks a ``cluster,'' ``collection,'' ``committee,''
``group,'' ``packaging,'' or ``selection.''
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