If you can’t solve the problem in front of you, solve an easier version of it—and then see if that solution offers you a starting point, or a beacon, in the full-blown problem. Maybe it does. What relaxation cannot do is offer you a guaranteed shortcut to the perfect answer. But computer science can also quantify the tradeoff that relaxation offers between time and solution quality. In many cases, the ratio is dramatic, a no-brainer—for instance, an answer at least half as good as the perfect solution in a quadrillionth of the time.
