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Solving Problems Imagine trying to cast 35 temperamental actors in a play. Some of them hate one another and won't be in the same production. Others will participate only if their friends are also hired. The result is called a satisfiability problem. Depending on the set of constraints that must be met, such problems can be easy, difficult or impossible. To get a grip on the situation, scientists plot various instances (think of each as a different play to be cast) on a graph. As a parameter called alpha is increased, the problems suddenly change from easy to impossible — like water abruptly freezing into ice. In the middle are the most tantalizing problems: those that are difficult but not hopeless.
Source: American Scientist
Credit: The New York TimesGo to Article
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