If Input Intervals are Narrow Enough, Then Interval Computations are Almost Always Easy
In the previous chapters, we have shown that in general, interval computations are NP-hard. This means, crudely speaking, that every algorithm that solves the interval computation problems requires, in some instances, unrealistic exponential time. Thus, the worst-case computational complexity of the problem is large. A natural question is: is this problem easy “ on average” (i.e., are complex instances rare), or is this problem difficult “ on average” too?
In this chapter, we show that “ on average”, the basic problem of interval computations is easy. To be (somewhat) more precise, we show that if input intervals are narrow enough, then interval computations are almost always easy.
KeywordsRational Function Lebesgue Measure Rational Number Rational Coefficient Interval Computation
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